Hey,
Under $500 is tough for 5.1 much less 7.1. My next question would be are you willing to just do 5.1? For reference nearly all games and TV shows are at most 5.1 and with movies 5.1 is probably still used quite a bit more than 7.1. I suppose I should also ask where you live, right now I'm assuming it's USA since you left it at $500. Also, I'm assuming HDMI or digital coax/optical connection.
Are you willing to add over time? This can make a big difference, $500 now and say another $4-500 throughout the next year can make a big difference in what you can get. A lot of people start with something like 2.0(1) or 3.0(1) and add later (which includes me, started with 3.1 because I was on a tight budget).
Right now, with just a budget of $500, you're mostly looking at home theaters in a box or something close to it, or going used.
HTiB's aren't necessarily a bad way to go, I don't want to you get that wrong impression here as it really depends on your expectations and what you'd like to go for. I'd say that a good percentage of people going for external audio are content with something that's better than TV speakers and/or having the surround experience. That's fine if that's all you are looking for. If you are looking for something that's a bit more theater like, then we need to do better.
Used can be a great way to stretch a limited budget, though it depends are where you live because if you need to ship it in, it needs to be a very good deal. However, this route requires time to look for deals and the knowledge to know what to look for, if that's something you'd like to consider, I'd suggest visiting
http://www.avsforum.com and do a lot of reading
. If you plan on asking for help, keep in mind that they can be rather persistent in (and unfortunately sometimes rude about) trying to increase your budget (which I guess I'm trying to do alittle here too), building over time is reasonable, but stick with what budget you want to do and keep them to it.
Just to get the ball rolling, $500, 5.1 and new:
For HTiB's I'd take a look at these;
http://www.bestbuy.com/site/yamaha-500w-5-1-ch-3d-home-theater-system/4372018.p?id=1219098067770&skuId=4372018&st=categoryid$pcmcat186600050005&cp=1&lp=2
http://www.amazon.com/Onkyo-HT-S3700-5-1-Channel-Theater-Receiver/dp/B00LU0GPAI/ref=sr_1_3?s=tv&ie=UTF8&qid=1413109317&sr=1-3&keywords=energy+take+classic+5.1
For something that's a little bit better:
http://www.amazon.com/Monoprice-Premium-5-1-Channel-Subwoofer-110565/dp/B00EOZFUYI/ref=sr_1_3?s=electronics&ie=UTF8&qid=1413109462&sr=1-3&keywords=energy+take+classic+5.1
With this AVR:
http://www.newegg.com/Product/Product.aspx?Item=9SIA1J70S50306
Prices will vary alittle from place to place, and whether something is on sale. If possible you'd want to get them from a place that's easily returnable/replaceable.
Out of those, my choice would be the Monoprice speaker set with the Denon AVR. However, I'd still strongly suggest considering the buying over time (or doing a great job on used) if you're even remotely looking for more of a theater type sound. If it's something you'd consider, give me a couple of budget's you'd like me to look at.