Lawnmower advice - small garden

Hi

I am new to this forum but also new to gardening. In fact I have never mowed a lawn or ever planted anything. However, i've just bought a new hous and am moving into it in the next few weeks and want to try to make some small but effective improvements to the current garden. The property has small back garden + even smaller front. In the rear is a flower bed behind a raised section brick wall (only a foot high)

My first step in the garden will be to cut the grass. For this i'm going to buy myself a lawnmower. I've had a cursory look at options such as a manual push type, hover, rotary and petrol. Given that i'm below novice level and have a small garden this should automatically rule out anything elaborate such as a petrol or rotary type
I am considering either a manual push or hover type which includes a collecting bin.
would either be suitable?
Can anyone give me any pointers on what to look for in a lawnmower?

Does grass cutting need to be done in a certain way? or is it simply a case of point and shoot?