Lawnmowers are a matter of personal preference really - if you want a formal, striped lawn, then one with cylinder blades and a roller on the back would be best. If you want something that will do the job quickly, even when the grass is damp, a hover or rotary mower.
As for the edges, not sure whether you're asking if you need an edging, or how to keep the edges sharp. If the latter, get yourself some long handled sideways on edging shears (there are two kinds - in one, the blades stick out at right angles to the handles, so they're pointing directly away from you when you hold them, these are for doing the top, horizontal few inches that the lawnmower doesn't reach; the other kind have blades which point left when you're holding them, and these are for clipping the very edge, where it meets the border). Do the edges every time you mow, and if you don't have time to mow, just clip the edges.

Can,t do any better than that Bamboo, lol. Derek

Ha ha - this'll make you laugh even more - I used to trim the edges with ordinary shears till about 10 years ago, when I discovered I'd be crippled for a month if I attempted to squat for a few seconds, never mind 'walking' while squatting, which I used to do... Oh, those were the days, when everything was easy and the elastic hadn't gone...

Know the feeling well, Bamboo, {and it,s not funny} Derek.