Powering Legacy Audio Speaker System

A receiver usually is an all-in-one unit.  It usually refers to something that has an amplifier(s), preamp, tuner, DAC, and controls video.  It will decode surround sound input like DTS, Atmos, etc.  It may also have a phono stage.  They are generally speaking, a swiss army knife built more for home theater than high quality audio.

An integrated amplifier typically has an amplifier and preamp but no video or surround sound capabilities.  It may have a phono stage and some have DACs in them.  Integrated amps are typically 2 channel and purpose built for listening to music.  They may have a home theater bypass function so that it can work in conjunction with your home theater setup.

I'm new to this so I'm a little unfamiliar with the difference between receiver and integrated amp.  

If you run your hdmi directly into your tv and optical to your reciever I would reccomend one of the older powerhouses like the Denon 5803. It's gonna sound better than any of the new light weight recievers anywhere near its used cost. Weighs 60lbs and is 170 watts a channel. Was over 4k new. 
Should be able to get a good one for under 400 if you look around. I lucked out and found a near perfect one in a Pawn shop for I believe $130. I also have a newer Denon 3808ci which was a $1600 receiver. The 5803 sounds much better. 

Check out accessories4less.  They have a number of receivers in your price range.  I don't have any specific recommendations as all of my gear is comprised of separates.  I'd look at some of the Yamaha offerings.

I was hoping to stay around $1000 for this.  Primary use will be home theater

Those speakers are fairly efficient, but they're going to work best with a lot of power.  A receiver could work and it would be OK for home theater and casual music listening.  You say you don't have the budget for separates.  What is your budget?

I would stay away from a receiver.  Are there any multi channel integrated amps you could look at?  Maybe a used Anthem?