(Not sure if you can see this if you're not a member of the Audiophile Foundation)
We had a recent "$2000 Budget System Design Challenge", and the results may be seen at: https://sfaf.clubexpress.com/content.aspx?page_id=5&club_id=794405&item_id=115420&
The rules were pretty loose, but they generally all include at least 1 source component, so the amp & speaker combos are at least in the kilobuck neighborhood.
You might also consider something like the Parasound NewClassic 200 Integrated Amplifier; they've got a couple used ones at $599 at The Music Room (NOT to be confused with the Parasound NewClassic 200 Preamplifier). They just slid a 110 watt/channel class D amp into the 200 Pre case, so you get a full-featured preamp (MM/MC phono, DAC, subwoofer support, HT bypass, remote control, preamp out) plus power. That gives you plenty of flexibility, and you can bypass any function later with a better external unit if you choose. The current Parasound model is called the NC200INT, new at $899. The company was sold a couple years back, so I think this is mostly just a re-badging. Of course, you'd need to buy a pair of speakers, too!
BTW, speakers are the most important issue. While I love the LS50s, I personally would never use them without subwoofing. Since I'm reluctant to get a subwoofer, I've always ended up with floor standers. Are your speakers currently on shelves, desktop, or stands? Are you willing to dedicate some floor space to them (whether towers or smaller speakers on stands)?