Hey
Welcome to Songstuff!
Well it's a big subject. Basically it's a good idea to get a decent microphone for a start (You could do worse than a Rode NT2), a decent channel strip with phantom power and decent EQ capability (Focusrite and Joe Meek both do some excellent gear), and I would recomend an outboard compressor (For budget check out the Behringer Composer), and a noise gate.
Other than that in either software or hardware a decent reverb unit (Rev 7 or later model second hand), a muli effect unit (Yamaha SPX90 or SPX 900 etc) are always handy.
You could also look at Antares Autotune for some useful features, and an aural exciter (Aphex).
There are lots and lots of decent PC based software effects programs too.
If you are using a PC as your recording platform, I would still consider the outboard noise gate and compressor. You should also look at a good audio editor, like Soundforge, or my preference Wavelab.
So how do you get a good sound? Well for a start don't record at too high a level. Leave yourself some headroom to work with.
Try and process the track on playback where you can, and leave the original untouched.
Most untrained singers have little control on their vocal dynamics, and little or no mic technique. Use a pop-blast screen (buy one, it makes a difference, or if you can't afford it -use a metal coat hanger and some nylons/stockings). Use your compressor on a soft knee setting to level the vocals out subtly.
Treating vocals is dealt with in several articles on Songstuff from EQ, to compression etc. You can read them in the Music Recording and Music Technology section...
(in the menu bar on the left of the main site pages)
I hope this helps!
Cheers
John