You need
1. A way of getting ok sound into the computer. i.e., a reasonable condensor mic, on a stand with a pop shield, a shock proof mount and a reasonable lead (XLR is the standard connctor format).

The blue snowball (£64) is probably as good a very low cost option as any. It connects via USB, so is very simple to interface.
The Rhodes NT1A (£127 including pop shield, mount and lead) would be my preferred choice, given your budget. It is a good low cost vocal mic, especially if you can get it at the amazon price quoted, but watch out for forgeries (this applies to any half decent kit).
A non USB condensor mic, like this will need an audio device of some kind to provide power and preamplification. Behringer make some perfectly useable high value mixers and audio interfaces at very reasonable prices (£30ish). Focusrite make better ones, but they cost more.

Adequate Mic stands can be purchased for something like £16-£20.They do need to be reasonably sturdy or will droop under the weight of a mic and shockmount.

2. A recording environment that is not too lively. It is perfectly possible to make a bedroom or living room acceptable, without spending any money (although you can, if you feel so inclined). I have always found items such as duvets, strategically placed, very adequate, even if not perfect. Remember sound reflections come from behind as well as in front and these are usually closer to the microphone and in its highest response zone. Plenty of good advice to be found online.

3. A way of processing the recorded signal to make it the sound package you want. The programmes that do this are known as DAWs. These turn your computer into a virtual multi track sound recorder with full editing facilities and the capability of introducing audio effects such as a touch of reverb to give your sound a bit of sparkle.
You may think you don't need more than than one track but you will soon find you do!
They will also allow you to export your completed track in a form usable by everyone and on any sort of (digital) playback device.

I use Reaper which is cheap (I think £60), easy to use and IMHO the best. I used to use Cubase (not cheap, rather quirky, but probably the best around at the time), I have used Cakewalk too (not cheap either but less quirky). There are others. Your real professionals prefer Protools but that will set you back serious bucks.

For you, though, your options are straightforward: Garageband for MACs. Audacity for PCs, Audacity is highly recommended as a "professional" quality DAW that will deliver everything you need or want and it comes absolutely free with no strings and no hidden drawbacks. Available as a safe download here: http://www.audacityteam.org/

When you feel the need to know more there is tons of stuff on the web but the items above are all you really need to get started.

Greg




There is a bit of a learning curve associated with all these but there's loads of excellent on line help.


! getting sound into your PC
a) Very cheap option: USB microphone (e.g., as recommended: The Devine Pro USB https://www.bax-shop.co.uk/studio-microphone/usb-microphone?utm_source=bing&utm_medium=cpc&ut)
This will plug straight into a pc with no interfacing but you would need some peripherals, including, at least, mic stand and pop shield).

b) Not so cheap but still affordable and heaps better: NT1A Condensor mic with audio interface (e.g., again, as reccomended   http://www.amazon.co.uk/RODE-NT1-A-Condenser-Microphone-Bundle/dp/B0002PSCQM./ref=sr_1_2?s=musical-instruments&ie=UTF8&qid=145054
This is a more than adequate vocal mic for the money and is a good choice if your budget will stretch.

2. A non USB condensor mic (like option 1b)) will need an audio interface supplying power for the mic (known as phantom power, standard is 40V) and preamplifying the mic signal to a usable level.

cheap but not too bad (I started out with something similar and manged ok):https://www.bax-shop.co.uk/analogue-mixing-desk/behringer-xenyx-502-pa-and-studio-mixer?utm_source=bing&utm_medium=cpc&utm_campaign=UK%20-%20Bing%20-%20Sound%20%26%20PA%20-%20Longtail&utm_term=xenyx%20502&utm_content=Behringer%20XENYX%20502%20PA%20and%20studio%20mixer