IMO you can get away with a 1/4" and 1/2" set. No need for 3/8"
1/2" kits go down to 10mm and 1/4" kits max out at 13-14mm.
Add in a ring spanner set or two (hex and 12 point, brand doesn't matter that much just it needs to cover +- 6mm-19mm )
10mm, 12mm, 13mm, 14mm, 17mm are the most used sizes.
As for brands..
Halford Professional is well made. Can't fault it.
My wrenching experience, summed up:
My daily kit that I use is a 2nd hand 1990s Teng 1/2" 43 piece set and a (new to me, 15 years old now...) 1/4" Teng meccarosso set. The blow molded cases hinges on these are going tho. I've got elastic cord around them to keep them shut.
In our family car we have a Facom SLD 1/2" and dinky Teng Meccaroso 1/4" since these are minimalist sets perfect for the road.
The Facom SLD 1/4 and 1/2 sets would be my 'go to' now as I prefer the form factor to the Teng ones. Better box. Not blow-molded. Higher quality sockets and mechanism.
I got a cracking deal on our 1/2" set 5 years ago, they're up in price now.
https://www.ebay.co.uk/itm/154773243868c 1/2"
Facom SLDBOX412 Metric Size Socket - 22 Piece 3148519048018 | eBay 1/4" still a good price tho.
The current version of my daily 1/4" Teng Mecarosso set - I use this kit at least once a week.
Find many great new & used options and get the best deals for Teng Tools Sale 36 Pce 1/4 Drive Sockets Deep Ratchet Tool Kit Metric at the best online prices at eBay! Free delivery for many products.
www.ebay.co.uk
If you use tools on the regular you'll learn to prefer some ratchet designs over others. The nicest one I've used Facom. Teng is good but not 'gosh, that's a nice mechanism' like the Facom.
Ultimately the cheapest sets will still 'do the job' but the better sets will last you a decade or a lifetime if you look after them.
Other kits to look out for that shouldn't cost the moon - Hazet, Wera, Wiha, Draper, Stahlwille, Bahco (Great adjustable spanners!) and Knipex Cobra Pliers (no toolkit is complete without these and a set of mole grips)
Left field suggestion ? Wurth! I've got a secondary 1/4" Zebra set and it's good, small profile, decent ratchet mechanism. Better than Teng.
The best screwdriver I've ever used was a King Dick 1-for-6 tho. And I never lost a 10MM.