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

I tried the LS50 / Meridian 556 combo and found them fatiguing. Considering the OP’s set up restrictions a set of nice headphones might be the best bet.

Listen for yourself, but I’m a big fan of the family of tweeters Polk uses in those monitors. Very extended and smooth.

 

I like Monitor Audio a lot but the tweets are not as neutral until you get to the PL line.

In that case, I could recommend the Wharfedale EVO 4.1 or 4.2. Add a Schiit Loki Mini EQ to tweak the sound to your liking in the bookcase. Additionally add isolation pads from Herbie’s Audio Lab to minimize vibrations from the bookcases. 
 

I have the EVO 4.1 in a cabinet in my kitchen and they sound quite nice. Surprising bass and the downfiring port removes thuddyness.
 

You’ll have a hard time getting a deep sound stage from the bookcases, but you can certainly get great tonality and enjoyment. Using pink noise and “tuning” your speakers to a flat response to your room with the Loki will help a lot .  I’ve done this in a few different/weird setups - really excellent device. 

FYI, rear ported speakers usually don't sound as good when placed up against the back wall.   Decades ago, before there were so many high powered amps, speakers were more sensitive.   Nowadays, with few exceptions, most speakers are ported and rather insensitive.  Take a look at the KLH product line.