SOFTWARE

If you feel like having a go at this sort of thing, there are some free programs available that will allow you to get a feel for it. I haven't used all of them so I can't vouch for them.

The following links, which worked when last tested, are to pages that are not part of my site:
There's an online version for you to try.
Jazz++ is an open source project midi sequencer. A lot of these open source projects originate from Linux.
Music Studio Producer is another free one.
Quartz is said by some to be the best free midi sequencer.

You will be able to record vocals with the sort of headset language training programs sometimes come with. If you intend buying one look for one said to be suitable for speech recognition software. It should be relatively inexpensive.

If you're a bit more serious then you need what is sometimes called a client, that is a midi sequencer that is compatible with software synths. On Windows, there are two main standards for these. VST appears to be the most widely available though there are also some DXi synths. Ideally you want a client compatible with both these standards.

For a home user the leading midi sequencer plugin clients are Cubase and Sonar. A visit to your local music shop is likely to secure one or the other. There are others, including Music Creator. You should be aware that some sequencing and synthesiser software, especially if it is aimed at industry professionals, may require additional hardware (usually sold with it) to be fitted to the PC it is running on.

If you're interested in using an Apple Mac, then there are three Apple programs you could use:

Garage Band. This fairly basic program comes free with Mac laptops. I believe it is included with the operating system. If you happen to have a Mac this is a good way to have a go at writing your own music. You can buy more instruments for it, and these should also be available to Logic Express or Logic Studio later should you decide to invest in them.
Logic Express. This is aimed at home users who are rather more serious and at time of writing retails at around £160-odd. I gather that Logic Express has been steadily pinching features from its big brother Logic Studio. It is compatible with plugins, but on the Mac the main standard appears to be AU (Audio Units).
Logic Studio. This is the full-featured product aimed at music industry professionals. At time of writing it retails for somewhere around £400. This still makes it much cheaper than equivalent Windows products. Although £400 sounds much more than £160, bear in mind that you won't need to spend much on expansion packs with new instruments before you would have been better off getting Logic Studio.

The advantage of Apple is that they are better machines, better made, with better designed software that gives better performance for the same spec. The operating system is much better. The disadvantage, apart from the relearning, is that they are expensive. At time of writing they start somewhere over £800 - plus any additional software.

If you're using a Mac then you may find these files (which I wrote purely to remember how to do things for my own benefit) useful:

My logic manual - this continues from where the official instruction booklet that comes with Logic Express left off.
Recording - this is a whistle-stop aide memoir of recording vocals with a USB microphone.
Printing covers - this is an aide-memoir of designing and printing CD covers using Disc Cover 2 by BeeLight Software.

You may also be interested in this. It's a summary of the upshot of musical theory - keys, some chords, harmonies - I did search for something like this on the internet. I did quite a bit of searching but I couldn't find it, so I compiled it myself. As far as I'm aware all this is correct but bear in mind I'm not a musical theorist - I got it from other places. It's in Open Office format.

Again if you're after higher standard recordings, you are likely to want a studio standard condenser microphone.

You can get a microphone that plugs into a pre-amp (which most professional microphones will be designed to do). In your case the preamp will be an external USB sound card but be careful that the plug on the microphone will fit into the socket on the sound card.
You can get a USB microphone that plugs directly into the PC.
You can get a microphone USB adaptor lead (one example) which allows you to connect an ordinary microphone into a USB socket, although what the signal level is like as it arrives on your machine may be another thing. If your microphone is not an XLR (which unless it is aimed at industry professionals it may well not be) you will also need a suitable XLR adaptor (again, one example).
A fourth alternative is to record into a separate recording machine.

Sceptical noises have been made about recording anything through a USB port, for various reasons including latency - that is, delays. This can be an issue for live performance but since timing is essentially arbitrary when recording it shouldn't matter.

The majority of my recordings have been made using a Samson C01U, latterly (while I was still using Music Creator, which I'm not now) recording into Audacity while simultaneously playing back the synthesised backing using Music Creator. There are three tricks to this. One, do not use the Samson SoftPre software pre-amp as this appears to have been the source of significant problems for a number of users and will disable the Windows volume control thus greying out the volume button. Two, set Audacity to record one channel (mono) and 16 bit only (not 32). Three, adjust the (now not greyed out) volume button to near or at the top of the scale.

You may also want to ask your music shop for: a boom mic stand, a pop filter (which should be a round soft mesh on the end of a flexible stalk) and a shock mounting.