Please recommend speakers <$800 for newbie

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?