Really what type of pedal to go for is rather subjective and depends on what type of ‘sound’ you are aiming for. Is it blues; rock;metal etc?. You might find some advice on the type of pedal in the effects forum.
If we tried to explain the differences, in words, between Overdrive and Distortion (and even Fuzz) it would be rather long winded or a bit too technical. YouTube is your friend; just search on there for Overdrive vs Distortion and you will find plenty. Ie. For one
https://www.youtube.com/watch?v=yj53Q-pisbwThe warning I would give is:- I don’t know the amp itself but I am assuming that it just has class D amp ie a Power Amp (a linear amplification device). That being so, a pedal might not give the expected results. Ttry and borrow one to check to see if the result is what you want. That, or spend as little as possible first.
The link in DarrellW’s reply to the Donner wouldn’t be the worst choice for the price. Be aware that mini pedals will need a separate power supply adapter as they won’t take batteries. So that would be another expense.
If you are looking for more versatility try a cheap multi-effects pedal. LeftyLoosy suggests the DigiTech RP55 – about £33 new. If your wallet will stretch enough then it may well be a better choice. It takes batteries (therefore cheaper than a mini pedal and power adapter), has built in tuner and will allow you to try out different effects. But get ready to spend hours messing about until you nail down the sounds you like. I am not familiar with this particular processor unit so for opinions on it try shifting this conversion to the effects forum.
Styrr