I can only echo what others have said about buying, servicing and street-converting a used rigid mountain bike. Fit fat slick tyres (they make a huge difference) proper fenders and some decent front and rear lights (you will end up out after dark at some point). A rear cargo rack can be useful as it gets weight off your back and onto the bike. It will do everything you want it to, and you can still throw some knobbly tyres back on if you feel like some off-roading.

For commuting, I carry a small tool kit, tyre patches (or a spare inner tube) and a pump- with a bit of basic knowledge, these will get you out of most mechanical difficulties you're likely to come across. Personally I don't feel a helmet is justified for everyday riding and commuting, but it's up to you (there's a dedicated thread with >200 pages of bickering if you're interested). Gloves can make the handlebars more comfortable to grip, and offer a bit of hand protection should you come off as an additional benefit.