Recommendations for modest budget

At that budget, I’d check out accessories4less.com for a receiver. Personally I’d want something 4ohm stable and with pre-outs (so you have the flexibility for upgraded speakers and/or to add a separate amp later if you want to). The Marantz SR5013/SR6013 are $500/750, respectively, and they are solid, well-featured receivers. At this price range, Yamaha is another that is often recommended. 

For speakers, the same site usually has decent Kef & Focal speakers in your price range. You should also check out SVS, which has good value speakers and subwoofers. Should be able to find a good combo for your price range with either. Don’t skimp on the center channel (it should be the same brand and model range as the front R/L speakers), but it’s fine to save money on cheaper surrounds. If you have room for and choose large tower speakers for the fronted R/L, then you can probably wait on adding a subwoofer until later. If you go with bookshelf speakers, then the subwoofer is more critical.

A few ideas...
Option 1: ($50 over budget)
Marantz SR5013 — $500
https://www.accessories4less.com/make-a-store/item/marsr5013/marantz-sr5013-7.2-ch-x-100-watts-a/v-r...
SVS Tower System — $1550
https://www.svsound.com/collections/prime-packages/products/prime-tower-surround-system

Option 2: (over budget by the cost of the surrounds)
Marantz SR5013
Kef Q series front R/C/L 
—Q750 towers — $1000/pair
—Q650c center —$500 (currently out of stock but should come back)
Cheap surround speakers of your choosing.

Option 3: ($250 under budget)
Marantz SR6013 — $750 
SVS 5.1 satellite system $999 (or upgrade to one of their more powerful subs)

There are tons of other options that will blow away a soundbar for $2k, but hopefully this gives you some thoughts and ideas to consider. It’s also definitely a matter of personal taste, so it’s always best to try to hear speakers before you buy if possible or get them from companies with decent return policies.

Finally, and I probably should have said this first, it’s important to think about how you’ll actually use the system. Do you listen quietly or loudly? Do you love that feel-it-in-your-chest rumble of the low bass frequencies or get annoyed by them? Movies and TV only or do you also plan to use it to listen to music?..if so, how... streaming, vinyl, CDs, etc and do you already have these components?  Several components to connect or just the TV? For under $2k you could get a sonos 5.1 system that would be nice for TV and movies and add the ability to separate out the surrounds to use on the deck or in other rooms when you don’t need 5.1... that’s definitely added value and a great option for many people, but it has limited inputs and the benefits of these and other “wireless” systems means you need a power outlet near each speaker and it’s not the best bang-for-the-buck sound quality vs wired options, so there are always trade offs to consider. 

Best set of luck!

Your $2K budget, is NOT adequate for a 5.1 system with receiver included. Simply being honest.

The tipping point is around 5K (not including cables or a basic power conditioner) for what you are considering. 10K ideally for a basic yet very good full 5.x.x system (which could also include a second sub and object channel speakers).

Aesthetics and setup of a 5.1 system are problematic AND you will encounter problems and costs you don't anticipate.

For your budget (negotiated price) consider this:

https://www.soundandvision.com/content/sennheiser-ambeo-soundbar-review

OR opt for a 2Ch system, for now, and build upon it when funds are available. This allows for very good speakers and receiver used (at $2K). Choose speakers that offer matching center and surround, etc. so you can add those at a later date.

I don't think that the OP is going to almost triple his budget and a decent sounding 5.1 system can be had for two thousand dollars, how do I know? Because I have one! Bought the speakers and sub used and grabbed a last year model of my receiver at a big discount because it was being replaced by a newer model.  Check craigslist for sub and there always seems to be a lot of home theater speakers on there as well.

Good Luck, TISH

For your budget, you should look for all used gears, used AV receiver & used speakers and used cablings, etc. Another advantage of buying used gears is most likely they are already fully broken in in the case of electronics & speakers, and fully burned in all the way in the case of cables. most likely if the seller had been using them for a while. 

Do you need an AV receiver that supports latest 4K HDR video pass through or not? I assumed you don't care about latest Dolby Atmos & DTS-X formats since you are only doing 5.1. Did you already have 4K/bluray player? Or is it just for cable TV DVR box/satellite TV, Apple TV & other streaming movie service providers? Most bluray and/or 4K UHD bluray players usually have built-in Netflix, Vudu, Hulu, etc. 

Are you going to be using your system for listening to music as well or strictly surround sound movies (HT)?