i would suggest a combi Drill & impact driver, probably cordless, but choose the range carefully, once you buy into a brand and battery sytem, its cost effective to stay with the same brand
I choose Dewalt and now have quite a range of cordless & power tools
The drill & impact driver, should help putting a shed together & putting shelfs UP.
Now for making things, like gates , etc
I would suggest a Circular saw , Jigsaw, Planer - I have all cordless and they have been brilliant for making, gates, fence, Windows seat and shelving
Not sure what would be needed for making banjos though
i used to shout the praises off ryobi as 70-80% as good as the big boys toys at 40-50% off the price i still buy ryobi as i have lots off there kit but i now choose dewalt by default as ryobi have upped there game and also the price to perhaps 70-80% off the big boys toys but because there batteries are more expensive per ah compared to dewalt 'dewalt becomes a good option
dewalt 4 and 5ah can be got for around 10-£12 per ah[45-48 4ah 50-60-5ah ] with ryobi seeming to be more like 15-18 per ah
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Once you have the basics, then buy tools as you need them and have a use for them.
Now I just need to take my own advice!
Remember, you don't need a power tool for everything. Some jobs are easily and quickly done with hand tools.
Making banjos comes under the heading of luthiery I'd have said.
Specialist tools and techniques. Mostly hand work, so although I don't know much about instrument making, I'd suspect that the power tools for general work won't be much used for that.
I think that starting out you should buy some used tools off Gumtree or Ebay to get as many tools as possible to get you going. I used to buy cheap tools with a view to dumping them but I am still using most of them 15 years on. Obviously it depends how much you use them but most tools are worth a punt. Do not be put off Lidl and Aldi tools either as they are very good I have found. Screwfix brands Titan and Erbauer are cheap but surprisingly good.