Welcome to the forum, Den.
I am sure you will get lots of conflicting advice, but here is mine.
Hand v power tools is very much a matter of time and temperament which are very individual. Power tools are loud, dust generating and, for me, unpleasant but they do get you there quicker. Hand tools are much slower but more satisfying if you wish to gain satisfaction from the process of making something as well as that you get from completing a project.
As a general rule, if a tool whether hand or power is very cheap, the chances are that you will end up buying it twice - the second being the more expensive one you should have bought in the first place. So it is better to spend you money on a few good tools than a lot of cheap ones and then add others as you can afford them.
For hand tools, my list would include:
150 mm and 1000mm non-reflecting stainless rules.
A Quangsheng No 4 smoothing plane from Worshop Heaven.
6 inch engineers square (all steel)
6, 12 and 18mm bench chisels from Sorby or Ashley Iles
Beech mallet.
Set of brad point drill bits
Veritas cutting guage
A Japanese Dozuki (double sided - rip and crosscut) saw. These are much cheaper than good quality European type saws (it's not worth buying anything less) and quite easy to master.
A cheap buiders merchant hard point saw for rough sawing.
A "scary sharp" sharpening film kit from Workshop Heaven. The cheapest and most reliable way to the sharpness levels you need to achieve if you do not want to get off to a frustrating start.
A subscription to British Woodworking.
All of these tools will be useful even if you go down the power tool route in the end because there is always some hand work to be done. You can reduce the cost substantially by buying used but you eill end up spending time bringing these tools up to standard and, for the novice, secondhand tools are a bit of a minefield.
For power tools, avoid the cheap own brand diy shed tools. The budget ranges of most of the well known names are fine but, if you can afford the pro range, even better.
You will need a drill. You don't need a big one. The latest generation 10.8 v lithium ion versions are excellent. Beyond that a router of around 800 - 100w from a reputable maker would be good as would a jigsaw. A bench pillar drill is invaluable as it is a sure fire way of reialble drilling holes vertical to a surface which is difficuly with a battery drill. If you don't have a bench, a lot can be done on a Workmate.
The first thing to learn is how to sharpen properly, tedious but vtal. There are some good demos on Youtube.
Good luck.
Jim