I'd say that a good starting point would be a Zoom B1 Four, think that they're around £65-ish new, £85-ish with the Expression (Wah) pedal.
The only downside to the multi effects, is that most of the preset patches tend to highlight what the effects can do, rather than making your playing sound better. You need to approach them as if you have a new single pedal, and find a good setting with that first, then move on to the next effect you want to try out. IIRC, the Zoom B1 Four is also compatible with their patch edit software, so you can plug it in to the USB on your PC/Mac/Tablet/whatever, and be able to edit effects on there. Another added bonus with them though, is that you can set up and amp/cab simulation for practising with headphones.
Individual pedals are somewhat less complex, but have a lot of trial and error before you find "the one", and that's before you start adding other pedals, pedal boards, power supplies, patch leads etc.
I think the "simple" Zoom pedals would be the starting point.