bassment

Electrum is quite simple once you understand the interface. The 16 buttons at the bottom are 1/16th beats. Choose a patch from the middle - e.g. choose kick, then do a basic four on the floor by pressing buttons 1, 5, 9 and 13.
Then select say snare and press 3 and 11.
Hit the the play button and off it goes.

From the menus you can change BPM etc.

Just for fun, using a Samsung S3 and a USB host cable, I can plug my Korg padKontrol in and play my phone using that!

I put together a setup for my home office space on a similar budget last year.

I'm using a Soundcraft Notepad 124 mixer http://www.amazon.co.uk/Mixing-Console-Channel-Price-For/dp/B0091H0SVO with a dirt cheap Pulse Audio passive DI cable http://www.pulse-audio.co.uk/5051259017658.shtml
This works absolutely fine for me - the mixer also takes the output from my Presonus firewire audio from my Mac, audio from my phone, CD player and freeview box (used as a radio).

Add to that a Carlsbro powerline 400 amp and Carlsbro monitor speakers (admittedly chosen mainly because they were on offer at CPC at the time).

I'm personally not fond of powered speakers - I'd rather have separate items that I can replace/upgrade as needed, and have more flexibility (plus I had space in that 19" rack that needed filling).

If you've got a smartphone, then try looking for apps for that.
I'm using Electrum Drum on Android - for £1.30 it's much cheaper than a dedicated machine, and you may well find that the free demo version is good enough. I'm sure there must be equivalents for iPhone, Blackberry or whatever.

Edit to add: I've also tried Caustic on Android, which seems far more flexible, but more complex than I needed.

If I'm practicing using my G01 headphone amp then my phone goes into the aux input and I can get the drum machine beat into the headphones.