My .02:
First and foremost, the best advice given by far by JonInc is DO THE RESEARCH. Learn about mics, the diff types, the pros and cons, what specs mean, how much they do or don't matter, the various brands, etc. You can get a lot of good info at gearslutz.com too FYI. Search that site.
- Wanting a "windscreen" (you probably mean pop filter) is frankly a poor reason to choose a mic. Most mics don't come with them but they are cheap. Get a mic because it's the best bang for your buck and fits what you're doing best.
- Also as stated by JonInc, it's a good idea to get an audio interface and an XLR mic (basically that means the type of connector it has, vs a USB...almost all mics are XLR). The good news is you can get a quality interface for as little as $40-50.
- You said "small budget" but that's rather vague. About what price range are we talking? You can get a respectable dynamic mic for as little as $50 give or take, a really good one for $100ish. Condensers (LDCs) typically will need at least about $100 or so, often more, but you can get a solid one for about that new.
- What kind of recording are you doing? Rock, pop, folk, rap, punk, Tibetan Blues?
This matters.
- What kind of voice do you have? A powerful, belt it out voice, or a softer, crooner voice? Something in between? This also matters.
- What kind of setup do you have? If your room isn't treated, you really need to do so. You can do this to at least a reasonable degree without spending much money FYI and it's the FIRST thing you should do before buying any gear.
That all said.....
With all due respect to the others, I do NOT recommend an SM58 or NT1A. The 58 is a great live mic, but for recording, you can do better for the money (I would suggest a Sennheiser 835). And I have not used but heard really good things about the ridiculously cheap Behringer 8500, but would suggest the isK ICDM as the best value overall ($60 and I think still can be had for the promo half off price, which is crazy for a quality mic).
As for condensers (LDCs), the NT1A is notoriously harsh on the high end. I'd look at the AKG 120 ($80), se X1A ($100), and Studio Project B1 ($120) for starters. Of course everyone has their favs. To get much better though, you'll realistically have to spend $200+.