Keep it small to start, can always build on your tools over time. You need a hammer, screw driver set (can be small primarily #2 Robertson (square shape, which is also red), #2 philips ( 4 sided diamond)). Those are the 2 most commonly used shapes and sizes here in Canada. Stud finder will be helpful so go for it, but I also suggest using break away butterfly clips for when you need to use a screw but there is no stud. There a but more expensive but are more idiot prof and better quality. Here's a link so you know what I mean. You don't need them for everything but if there holding weight I recommend.

https://www.homedepot.ca/product/toggler-1-4-in-snaptoggle-anchors-10pcs/1000695135

Get yourself an adjustable wrench which will help withe toilets, and facets. Other then that, het what you need as you need it. Congratulations and good luck!