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I've not long since started my quest to 'spot' every unit in mainland UK (shameless plug), so hopefully I can offer some starters for ten.
As Harbornite says, all you need if you're purely after logging units/locos, is numbers. Some are easy to get, such as EWS 66s or 150s, some are an absolute devil to observe, notably 220s, 221s and 390s!
I have a slightly convoluted approach to noting down numbers, which varies depending upon where I am. If it's a quiet spot then I simply log them directly to my spreadsheet on my phone, which automatically flags duplicates (I'm not interested if I've seen it before). If it's somewhere hectic, or the phone battery needs conserving, then I use a wee notebook, and transfer numbers across to the spreadsheet when time then allows. The latter method does throw up more duds, but I can at least filter them out later on.
To track overall progress I heartily recommend Trainlogger. I've paid for full access, but even the free version is good.
Can't go wrong with what Harbonite has said, and was how I started.
Although what always helped me are a set of books by someone called Robert Pritchard, published by Platform 5 Publishing Limited. First used these 10 years ago when I was around 7. Essentially there are 4 books which have a record of all the UK's trains. When you see an individual train, you can highlight it in your book. The books tend to cost around £5 each.
I also keep a little red notebook organised by date - any trains I see or ride I log in here, and then transfer into the books. I've only started to do this again recently, as I had a break from it all for a few years.
You will find quite a variety in what people log down.
At one end of the scale some just take photos, at the other you will find some that have small tape recorders and record not only the loco number but the numbers of all the wagons or coaching stock as well.
In the end most fall somewhere in between. I for one restarted 'spotting' about 10 years ago, and bought myself a really good quality notebook and pen, and I like to keep a record that can be of help to others sometimes, but mostly as something to look back on as the years go by. So I record the location, the date and time the loco number, head code, where it is from and going to and the name of the train operating company. I then transfer the number into a spotting book, such as the Platform 5 books.
In the end I think it is worth thinking about it a bit (as you clearly are) and decide how you would like to do it.
Log whatever you want - there are no rules and what works for one doesn't work for others. Asking here will get you all kinds of complex, obsessive and fantastical "rules" or approaches! Just decide what is best for you and go with that. Straight forward is always best to my simple mind.
ObviouslyI doesn't spot trains. Although I might take the odd picture
Don't know how your knowledge is but you've got to learn train recognition and to some extent the companies that run the services/freight. This will help with locations. I also had the platform5 books.