What prices are you actually talking about?
I'd suggest an adequate multimeter for typical electronics use (low voltage mostly) must have autoranging, voltmeter mode, ammeter mode (and a lower current ammeter mode too), ohmmeter mode (really vital), continuity testing, and approximate capacitance measurement. Pricing would usually be in the £30 to £50 sort of range. Any no-brand with these specs bought from a real electronics supplier (Mouser, Farnell, RS, Digikey...), not from amazon or ebay which sell utter rubbish no-brand ones, should be good. A duratool one with those specs and that price range should be fine enough too.
EDIT: I think the meter I use a lot is a D03041(it has no branding marks on it, but the internet photo ofone of those looks just like mine), works fine.
The thing you'll need other than a multimeter will be an oscilloscope sooner or later, those are rather more pricey unless you get a basic USB one.