Music isn't going to benefit from 7.1 (or 5.1, really) 99.9% of the time. Unless you happen to have one of those rare surround sound albums, that won't really matter.
For gaming, you can see benefits from both. To be pretty honest, I lean in the "7.1 is overkill" direction, too. I've never felt that 5.1 wasn't immersive enough, and with 7.1 you're pretty much running speakers and wires all over the place.
Even if you're interested in Blu-Ray movies, almost everything is still geared toward 5.1 setups.
I have some spare old speakers and tinkered with 7.1 briefly, but just found it to be pointless and cluttered.
7.1 is awesome for gaming when games support it. Some games (Arkham City, Sleeping Dogs, Borderlands 2) use crap like Wwise for the audio engine and Wwise doesn't support anything over 5.1 surround and then some developers are lazy and, while they use an audio API that supports 7.1, the game only supports 5.1 (Skyrim and XAudio2).
If you have enough room and properly place the 7.1 speakers then it's nice; having that extra set of speakers is nice. I pay a lot of attention to sound and, particularly in first person shooters, having the extra channels helps you locate people much quicker.
Finding a sub-$300 set might be difficult. I'd recommend an Onkyo HT-S5300 but it goes for $400. The speakers are better than skimpy cube speakers in that they actually have some mid-range to them. The receiver itself is good and you can upgrade the speakers around it; no proprietary connections so you can buy whatever speakers you want if you want to upgrade them later. Maybe find one used.
Like I said, if it's properly setup, you'll notice it. Follow the instructions that show where to put the speakers, set your sound device in Windows to 7.1, don't use any fake surround matrixing, and it should sound good in games.
If you pay attention to sound, then you'll probably like it but if you don't really listen to the details then you probably shouldn't bother.
edit: Oh yeah, if you do go with just 5.1, Onkyo has 5.1 setups for less than $300. HT-S3500 and HT-S3400. I like these because the receiver is good and there are no proprietary connections so you can upgrade the speakers later.
If space isn't an issue the receiver route is the way to go if you really care about sound. You can start with the receiver and 2 speakers and build from there once you have more cash. If you plan ahead you can get cheaper speakers from a brand you like and later on upgrade and move the old speakers to the sides/surround.
If you don't care about sound that much then an all in one bundle will be just fine.
Energy Take Classic package ($150 when on sale) + a budget sub + something like a Denon AVR-1612 would run you about $450 and it'd be a solid step above one of the Onkyo HTiB package, though those are decent... I agree that starting slow (receiver + two decent bookshelves) might be the better route, but the Onkyo packages give you a good starting point too and a feel for how you wanna set up 5.1 in your room etc.