Almost every drone has Pilot 3. Controlling (well, giving orders to) that drone isn't hard - they're ment to be used, and your character has some (granted very basic) skills at computers. It's not even a skill check normally if I recall correctly, and not many GM's will ask for a roll if you have the relevant skill.
Like Kincaid said, you'd probably be better off letting the pilot handle the drone itself. It'll have 3 to 9 dice - 3 from pilot, and 1-6 from the Autosoft running on it. Obviously you're going to want some. Comtrolling it directly is an option, but it'll use your skills and abilities. Shooting with it will use Logic, so that's not going to be a thing, but flying and perception uses reaction and intuition as normal so that should work fine - if you have the skill. (This does use your commlink's rating as a limit, so you'll need a decent one - but you want that anyway for the firewall).
Autosofts are expensive, at 3k each. For a combat drone you'll probably want gunnery and piloting and/or clearsight. Buying a decent drone and weapon, plus a smartlink, will set you back quite a bit of nuyen, and you'll end up with a dice pool of 10. It'll also get shot up fairly easily. All in all it's not exactly the most cost-effective firing platform, especially since you don't really have any options to improve it or utilize it more efficiently, but if you have nuyen to burn an extra gun on your sight isn't a bad thing.
Making it look old and scrappy shouldn't be too hard (although it introduces it's own problems if you're flying around with it), but it's still going to be an expensive combat drone. And people are going to recognise it as such. Even with a decent commlink, protecting it from matrix attacks will be difficult, and there'll be plenty of people wanting to physically 'inspect' your non-shiny toy.
All in all I don't think it's the best idea. But possible? Sure.