It looks like a standard generic number 4. It looks like Hilka are still operating: https://hilka.co.uk/no-4-jack-plane-43909504.html
It should work fine. Check the bottom is reasonable flat, and give the blade a good sharpen and see how you get on.
Do you already have any chisels?
If yes: You don't need many chisels. 3 or 4 will be enough for most jobs. On your budget (£60?) I'd buy two good chisels. 1/4" and 3/4" perhaps. Ashley isles are in that budget and excellent.
If no: I'd recommend buying a cheap set. I started with a set of...
I bought a second hand 6030 recently and am really pleased with it. It's definitely a step up from my DBO180Z. Much less vibration, and with a vacuum attached it produces very little dust. It is a very effective sander.
The Veritas saws are a very affordable pathway into hand saws. I prefer the older style saws, but a new one is likely to cost you at least twice the price of the Veritas.
The cheapest route is second hand, but there is a lot of variation and I think you need to learn to sharpen saws before you...
Hand saw for small bits would definitely be my recommendation. Japanese saws are a popular solution, but I'd recommend a crosscut carcass saw. Something like the Veritas carcass saw would be a good start. And the first thing to make using it would be a bench hook.
Even if you eventual do buy...
OK this is how it works:
You will buy things and you will never use them.
You will buy things that you will initially think are fine and later find better alternatives.
You will buy things because you think you will work one way (or build one type of thing) only to find that you end up going in...
I had a Stanley B6CC304SCR523 (or very similar). Worked fine - I changed the connectors to match my tools (a very simple thing to do - unscrew one, screw in replacement).
The only problem I had with it was that it was very noisy. Disturbed the neighbours noisy. Even from inside my garage.
When...