Please recommend speakers


I’m just starting my audiophile journey and want to make sure I pair the right equipment before going too far down the rabbit hole. I am coming into this as a complete newbie. I listen pretty much to everything but mostly pop, classical and jazz in a fairly large-ish lower level living room (maybe 20 x 20 feet square) and speakers sitting on bookshelves. I know they should be on stands or floor-mounted, but that doesn’t really work for me right now space-wise. So far I have Jamo 803 bookshelf speakers with newly purchased SMSL DA-9 amp and matching SMSL SU-9 DAC (previously was using an old NAD D 3020 V1 integrated amp with direct connection from iPad to internal DAC). Now I stream directly from an old iPhone/iPad via a USB camera adapter to the DAC which has balanced connections to the DA-9 amp. I pretty much stream music exclusively (currently on free trials with Tidal and Amazon HD). No other sources. No library to speak of. No headphones. The Jamos sound great to me, but I feel like I need something better to pair with the mid-fi DAC and AMP. So I’m looking for upgrade the Jamo 803s which were purchased on sale for $130. Looking to spend up to maybe $800 for a pair. Recommendations? Thanks in advance!

 

Edit:  Here's what I'm considering so far.  KEF350, Polk R200s, Audio Monitor Bronze.  Thoughts on pros and cons?  Anything else?

expresstrain
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If you buy used or demos you  could probably find Monitor Silver or Revel M106. You can get more for your money that way.  Having them on shelves you might look at studio monitor isolation desktop pads or stands. Try to get the front of the speaker to stick out a little beyond the shelf as well. 

Lol, I knew I should have left that part out.  I have a feeling I will end up getting stands also, but it's a process...  

Mini Lore monitors.

Tekton are the high value choice. These are 95dB. What that means is they will sound good and play quite loud even with a fairly low power 20wpc amp. It is kind of pointless trying to fill a large room with bookshelf speakers. Much better to max out on what you can, which with these and a nice little tube amp you can get quite good sound when sitting near, and positively passable sound everywhere in the room all other times. 

That old amp will probably be next on your list to upgrade. Buying high sensitivity speakers now will make amp selection later a whole lot easier. You could for example get a little Decware 6w amp and be happy as a clam with sound like you probably never heard before. System building. Way to go.