ebay for second hand older amps. same quality, but cheaper. alpine are good for amps, if your just running a sub, grab a monoblock, trying to match the rms with the sub.
as for subs, type r alpine, vibe blackair (i got 2 of them, awesome!).
you can get 10" subs for hardly anything off ebay. i got one for 99p!!! also got 2 alpine type E 12" subs for like £20 in custom boxes. so there are plenty of bargains on ebay. you can set yourself a good sub setup for £50. will be fine for your use, as you said just a little bit of bass to add to the sound. not sure how much you like your music (D&B???) but if you love it, you will probs get more bass LOL!!
stick to 10" for best sound quality.
LL