Different Tubes and general purpose?

I’m trying to get a better midrange push or clarity out of my Line Magnetic 501ia tube amp.   Can someone help me understand what the specific function each type of tube performs in a power amp?  

I would like to upgrade several or all of my “stock” tubes but would like to understand where to start to beat enhance each aspect of the sound spectrum.   On my 501ia i have 4x KT120 and i believe those are power tubes, but please help clarify if wrong.  There are 2x 6SN7EH 1x 12AU7 and 2x 12AX7 (but the AU7 and AX7 look interchangeable to me).   As i look to upgrade where to i look to start, and why?  
Thanks in advance for help. 
Another hack:
But, Miller is blathering about his favorite fuse vendor.

Blather? That’ll be the day. Point out the blather. If you can. If not then guess what? You are the one blathering.
I won’t argue whether a fuse can make a [slight] difference or not.

I see. So what will you do, then?
When I tried an aftermarket fuse, there was no discernible difference.

"An" after market fuse? Really? Which one? Sounds to me like you’re trying to call me out without having the integrity to admit you have no idea what you’re talking about, because you’ve never even heard a SR Orange Fuse. Right? More blather.
That was MY experience.

Right. Your experience with.... what? You haven’t said. More blather.
But, there is absolutely no way that a fuse can have a bigger impact than rolling tubes.

Based on... what again? Oh yeah. Your experience with "an" aftermarket fuse! Brilliant!
Rolling fuses would be low on my list of improvements to explore first.

Based on.... your experience with.... ?
Look at Miller’s system on AGon, and note that he isn’t even running original tubes.

OMG! Not even aware tubes do wear out and need to be replaced from time to time! Let me fill you in: even the original manufacturers tubes do indeed wear out and need to be replaced. More learning, less blathering, okay?

They have a sticker on them from theTubeStore.

Thank you, Inspector Clouseau.
They are still KT88s, but I think those are the only tubes that amp can run.

Correct. A dazzling display of blather.
In the big scheme of things though you will hear much more difference changing the fuse inside the amp than changing the tubes.

This is a gush, this is dismissive....this isn’t "correctly pointing out" anything....this is opinion that is dismissive of anyone else’s experiences that they wish to share. 

By the way, I never refer to anyone who lends an opinion as a "hack".  Who does that? Seriously???
Per the OP"

"Can someone help me understand what the specific function each type of tube performs in a power amp?"

This has yet to be answered...

Which pair of small signal tubes drive the KT120's?

I've seen 12ax7's commonly used as drivers, but I've also seen 6SN7's used as drivers in SET amps.

Though driver's can greatly affect the sound I suspect that the OP would be better off rolling the "other" input pair of signal tubes for starters.

Not much on the WWW about this particular model/amp that I came up with.

Thanks Dekay for the follow up.  That has yet to be answered and i honestly tries to research this, but struggled to find anything authoritative.  It would be helpful to know. 
Hello @gunners01

I have the Line Magnetic LM-508IA and tubes made a big difference in sound. In fact, power tubes (805 in my case) also made a considerable difference, may be even more than preamp tubes. 

If Im not wrong, you said that your amp has 50 to 60 hours of use. I would burn more the amp as I believe its not enough to judge its performance. In fact, during burning time, one day may sound worse than the day before. I would burn it at least for 300 hours before changing anything. 

Then, if you want to roll tubes, I would start with the preamp ones, wich are cheaper and can give you an idea of the changes. 

By the way, Ive tried changing the original fuse with a HiFi Tuning Supreme one and Ive found an improvement, but not huge. I would start with preamp tubes after 300 hours of burning with out a doubt. 

Good luck!!