If < ~2MHz and budget is everything, this sort of thing will get you started http://www.ebay.co.uk/itm/272267647631
These guys have iterated on the RTL stick a bit, though expect to pay a bit more: http://www.rtl-sdr.com/buy-rtl-sdr-dvb-t-dongles/
If < 8MHz, try this http://www.sdrplay.com (Not an RTL stick, performance FAR better. I own this, it's great.) I notice they have a new model out.
Above that, sky's the limit. Filters are possibly useful on the TV stick but by no means essential.
Antennas - all depends on proximity. If you're in the same room as your RF source, a bit of wire will do, for all but the weakest signals. Beyond that, it depends what you're doing.
My recommendation: Buy the £7 stick, see if it gets the job done for you. If not, try the SDRPlay unit. I own both, they're both good and will likely get the job done.
Software: HDSDR http://www.hdsdr.de/ SDR Console http://sdr-radio.com/ (current beta is excellent with SDRPlay RSP 1)
No affiliation to any links posted.
The rtl-sdr about page has a comparison chart showing various receivers a quarter of the way down the page...
It'll do 500k-1.7GHz, I've used it with this software (urh) as well as gnuradio, works fantastically!