"I just don't know what my options are then if I don't want to spend more than ~$100 on an amp alone and still be able to eventually hook up a sub to it."
The ONLY decent amps I know of under $100 are t-amps. If you want a good digital receiver with bass management for a sub then you'll have to pay more. You may be able to find a Panasonic sa-xr55 for $150 - great product with digital inputs. Maybe someday we'll get some high quality digital amps with bass management under $100, but to my knowledge there are none yet.
As for the comment about budget speakers not giving the sound quality of headphones, I have to disagree. Headphones excel at some aspects of sound quality but are terrible at others: principally soundstage and long term comfort. Overall, I think the experience of listening to a quality but inexpensive speaker system properly set-up far surpasses the experience of headphone listening. I'm sure others will disagree, but at best it is a debatable point because both have tradeoffs.
If I were you, I would get a t-amp with a proper powersupply and enjoy the speakers. If you later need a sub, you can decide between finding a sub that will work with a common ground, buying a box that fixes the common ground issue, getting a preamp and using low level passthrough, or getting a digital receiver or different amp. We're talking about a $50 or less purchase - no point in agonizing too much over it.