A wet and dry canister vac, yes, and get some disposable paper bags to go in it, they will delay clogging of the filter. Get a spare cartridge filter. You can dry brush the pleats, and once it is thoroughly clogged, you can wash it. Keep the spare handy to swap when you get clogged. If you can't get bags and filters to fit, don't buy it.
A builders vac is cheaper than a karcher.
If you get a cheap one with a 2-year guarantee, you are likely to get your money's worth before it goes wrong.
Don't get the smallest one.
They are rather noisy so buy ear-defenders.
Never allow a builder or DIYer to touch your household vac.
www.screwfix.com/c/auto-cleaning/wet-dry-vacuums/cat810212#category=cat810212&sort_by=price
This one has a power take-off socket which is very very useful with a power saw or sander.