I used Ikea cabinets in my garage when I refurbished it. They’re doing okay. I also built my own workbenches. If I was doing it again, I would probably just build the workbench and then use actual garage cabinets above and drawers that roll in underneath on wheels from a garage-specific company, so you get standard sizes, accessory drawers, etc.
Here’s garages I like. You might get some ideas from it:
Ive got a sealey tool chest, and have a few observations.
They fell well built, especially for the price, but
The draws are smaller than i expected
The draw bottoms are fairly thin, so they curve a bit and catch on the one below
The runners are riveted on, so if something moves in the draw and blocks it opening you have to poke things in to move it (the facom set i had at work the draws unclip)
The draws are meant to lock when the lid is shut, this doesnt work all the time (though its only an issue if you are doing something like putting it in a car, or actually want it locked)
Overall, im still happy i got it, but thought id warn you of these bits
For drawer storage I have two old battle ship grey steel Bisley A4 drawer cabinets, a 15 drawer for smalls and a 6 drawer for spanners, sockets, pliers, grips etc. Picked up the 6 drawer for free from a hospital skip and the other for peanuts off eBay. They don’t look pretty but a rattle can can sort that, what they are is sturdy.
Try Freecycle type sites, there’s always people getting rid of kitchen cabinets, worktops, etc.
For specific tool storage, Halfords are usually decent value for money & there’s usually offers on them. I have some of their ‘Industrial’ range, which are nice, but they don’t seem to do them anymore.