Which is more important?

I would like to take my system to the next level. What ever that may be. It is my understanding that any component can influence the sound as much as any other. Being economicaly challenged, upgrades are few and far between. Therefore my experience with new equipment in my system is limited. Plus, being in the military my listening room is always changing. Reviews are no help as preamps, cables, IC, and everything else seem to take a back seat to amps and speakers. Without rebuilding a house that belongs to the U.S. tax payers. Louis
Without a doubt, the right amp will provide the biggest musical performance gain over any other component.

This is assuming, of course, all of one's components are at least of minimal quality. (I feel obligated to qualify my statement above for any potential squirrels and nuts)

You should be congratulated for having put together a nicely balanced system. To really take it to the next level would involved a complete change out of components and the expenditure of fairly large sums of money. If you are serious it might help for you to explain what your system doesn't do now that you think it will do when taken to the next level? If there's something specific, then tell us. It's very easy (and somewhat dangerous/frustrating) to just change components and change the sound of your system. In order to cost effectively take it to the next level requires that you to have a specific goal in mind.
Recently I have been doing the exact same for my system. How do I get it to the next level. I met someone who is a true audiophile and has had more and has more equipment than some dealers that I know. I got to meet with him and hear so many of the major speakers, amps, preamps and CDPs that I always wanted to hear but did not want to deal with the local dealer. The first step is your speakers. You need to know that they are providing you with the sound YOU prefer, not anyone else or what a reviewers says. I had a room issue since I only have 7 foot ceilings in my dedicated finished basement so some of the large speakers I would have liked simply over powered my room. My friend lent me three different pairs so I heard it first hand. I could have used a Rives room correction device and I will get one at a later date when I get more funs.

Next in the system is the match between your speakers and power amp. The amp has to be able to drive the speakers. I originally had B&W 803 matrix II speakers in my system although they are 91 db, they do not work well with tubes versus SS amps (in my price range as I am sure there are some really good tube amps that would have worked well).

Once you find an amp that mates to your speakers, you need a better source. I was using the Sony SCD-777ES in my system as I only use digital as a source and I always wanted to try the better CDPs or modify the Sony. Well I have a Wadia 861, EMC-1, Audiomeca Mephisto II.X and a highly modified Shanling CD-T100 (custom mod past what the level one + mod offers). These while different sounding, made the biggest overall change in my system.

I added the Talon Raven-Cs in my system and I was getting a harshness that everyone (Talon dealers) were telling me was the mismatch between the Pass Labs gear and the Ravens). Well than may be so by my friend to me that the biggest change would come from adding a better source first so that is how I got the different CDPs to try out. Well with the better CDPs especially the more analog sounding ones, the brightness/harshness is GONE! Now I can find an amp that will add to the sound (I know not what I said above about map matching first but the Pass is good in the system and now I can hear what lacks in the system better than before so a different amp may help to add or subtract from the sound I am now getting). When I had the B&Ws, different amps and preamps did not make that big a difference. I should have changed the source but I was not hearing the harshness in my system with those speakers.

Last preamps. The preamp function is really a volume control which works to remove loudness and not increase loudness, so you need to find one that does not change the sound of your system at different volume levels.

Cables and room treatment are also in the mix somewhere as well as speaker positioning and isolation.

So I hope my experience has helped as I am now fortunate to be able to take many amps, CDPs, preamps and cables home to try without any hassle and really spend time to see what makes the biggest improvement. System synergy is the key to building a good sounding system no matter how much you have to spend on components.

Happy Listening.
Your biggest problem is the ever changing listening room.

Suggest you look for a Tact 2.0 room correction system. It will allow you to get the most out of both
your system and the listening space our tax dollars have provide for you.

PS- Thanks for serving your country.
I lived in a city that had an army base once and the local pawnshops usually had good selections of audio equipment. When someone was transferred out,they sold their stuff that would then get bought by guys(and women) who transferred in.

It seems to me that with the mobility needed to serve in the military and what you said about different listening rooms,using the shops and audiogon make sense.

You can figure what you want,what you can afford,and put together a temporary system-knowing it will be for sale in a couple/three years.
Ah yes,that wonderful government housing! For a reasonable amount of money you can get a good set of headphones and more importantly a headphone amp. You'll get awesome sound that wont change when you move! When your a free man again
(har,har) you can start building a real system. This is also good for not pissing off the wife and neighbors.
I agree with Onhwy61 - you need to assess your systems shortcomings and develope a plan. Were I you I would get the best neutral monitors & amp that I could afford, and a good sub woofer. (If you are happy with your speakers and amp as they are then perhaps you should do nothing! Its all about synergy). This would allow you to move from quarters to quarters without having to worry much about room size etc. Once chosen I would let those components dictate future changes, that is your pre-amp and CDP. Your turntable set up is just fine as it is.
Nice system, you could play around with some tubes for something a little different..But, the next level for you is small steps as your system has gone past mid-fi level IMO.

I would also note that with your present quarters you have the same problems many apartment dwellers face and a total and lasting fine tune of the system is not $$$ something you may like to do in someone else's space.

Do you have good speaker stands? Onhwy61 has some pretty good advice for you IMO.

Resonance control and speaker placement. This can be done very inexpensively per many of the threads here. Try cardas.com for placement recommendations and try any number of resonance tweaks, including even the very cheap. Oh, and lifting your cables off the ground is huge along with proper polarity (see the Wood Effect book)and isolation.
I know most, if not all my problems come from my listening/dining/living room. The sound is a bit bright and thin. The sound stage is not bad considering the area, although a bit narrow. Plenty of detail. I think what I am looking for is a sound that is a little more rich, full and engaging. I am not great at describing what I hear, but I know what these components have the ability to sound like together and separately. And I know it could be better. I am also surprised that as great as the Nottingham sounds it does not "blow away" the Pioneer, as it should. I know this table deserves a better cartridge. Is it possibly the Rega reviews are some what exaggerated?
The room and speakers together are the most important component. The two interact and should be viewed as a system. Room gain can supplement the bass of a smaller speaker or make a big one too bloated. How the room reverberates can determine how bright/natural a speaker sounds.

You can't have speakers that are too good. The used market, internet direct sales, and DIY construction of projects by _good_ designers can all keep the price tag reasonable there. However, a sub + monitor setup will give you more placement options to work arround poor rooms.

After that, things to minimize your rooms' effects would be good. A Tact room correction system, parametric EQ for the bass, tapestry you can hang on the wall to kill high frequency reflections, etc.
Get A good line conditioner AND most important if your components have detachable power cords, upgrade these. They
will come in handy when you are ready to venture out of the Military since even good components come with stock power cords.