Hello and welcome
Your receiver should be fine for now.
Just a quick suggestion for the physical layout of your setup: try to pull your couch away from the wall behind it. Having about 3 feet or more from the back of your head to the wall behind you would be best for your audio, but even if you can get just 1-2 feet of distance from the back wall, that will improve the sound you hear as compared to having the couch right up against the wall (which is what most people have
). Most people don't notice just how much sound is reflected off of the wall behind them! When you put a gap between the wall and the couch, you get a fair amount of that reflected sound being absorbed by the back of the couch now, rather than being reflected directly back into your ears - which muddies the sound and makes dialogue more difficult to understand.
That done, I would really highly recommend the
Onkyo SKS-HT540 speaker package to you!
At $250 from Amazon, it certainly fits within your budget. This is not a "dream" system, of course at this price. But it's remarkably good for this little money and what I like most about it is that, while inexpensive, the speakers are still a genuinely good, basic design. So many inexpensive speakers these days are terrible from an audio design standpoint because the only goal is "fashion" looks and tiny size. These Onkyo speakers are actually pretty big compared to a lot of other speakers, but their design is genuinely decent from an audio standpoint and every penny went into doing the best possible design for the sound and not the looks at this low price point.
The included 10" sub actually packs some decent punch. More important though the bookshelf speakers play low enough that they blend really well with the subwoofer. Overall, this is absolutely the best sound you can get at this low price point and I consider this SKS-HT540 package to be a terrific "foot in the door" system and one that will keep you happy until you are able to afford a full blown "dream" system
You'll note that this is actually a 7.1 speaker package. Obviously, for your setup, you don't need or want to have the 6th and 7th speakers behind you. Stick to using just 5 speakers and the sub for now. But you could always use the spare 6th and 7th speakers in the bedroom or something
Finally, when living in an apartment, what usually gets complaints is the bass. What a lot of people don't realize though is that the bass the neighbors hear is mostly structure-borne bass and not bass travelling through the air. In other words, with the subwoofer sitting directly on the floor, it actually couples to the floor and physically shakes the floor structure. Structure-borne transmission of the sound is what makes bass so easy to hear all through the entire building!
So if you want to reduce complaints and make it so that you can actually use the subwoofer properly and hear some bass in your room, what you need to do is decouple the subwoofer from the floor. If you're willing to spend $50 and spend your full $300 budget, I can VERY highly recommend getting an
Auralex GRAMMA to put beneath your subwoofer and decouple it from the floor.
A lot of people wonder, "do I really need a decoupling device when I'm using a low cost sub?"
The answer is - yes...even more so, in fact!
A lower cost sub typically has less internal bracing, it's often lighter in weight and it's often somewhat less optimized in its design. In other words, inexpensive subs tend to shake and flex more than expensive subs and that means they shake the floor beneath them just as much or more!
Decoupling your subwoofer makes such a huge difference, not just to the sound you hear yourself, but to reducing the bothersome bass that your neighbors hear. It's worth every last penny of the money you pay, but I could understand if you feel $50 is, percentage wise, too much to pay for use with a $250 speaker package. It's totally worth it, IMO, but I could understand.
So if the GRAMMA is a no go for you, you can still try to decouple the subwoofer with some other means. Placing a couple of mouse pads under each foot of the subwoofer works pretty well to decouple the sub. You can also use any sort of rubber pad - like the kind they have on a gym floor. Basically, you just want something that will act as a physical buffer between the subwoofer and the floor
Best of luck!