Cycle in jeans, roll them up if you wish.
Bell is a good name. Computer wise don't know. Cadence is the real deal, you want one that shows candence. Strada Cadence by Cateye is good. $35.. Otherwise if you want cheap computer find one on eBay.
As far as helmet, Bell all the way. Get a cool looking helmet. Bell mountain bike helmet and Sweep XC are pretty much coolest looking helmets from Bell. Others don't look that good. One is $25 and the other $90+. Again eBay.
You going to need cages and bottles.
A pump with a hose. Don't get small pump without a hose. Get a good pump, such as Topeak Road Morph or the like, the one that has a hose with it.
Get a saddle bag, wedge bag. For holding a multi tool, a spare tube, and a patch kit. Plus a pair of gloves and a plastic pulix bag for changing tube and carrying old dirty tube once changed.
A light is a must. But beware, most lights (tail lights) a plastic and fall off when the bike falls off.
Your most important equipement are your shoes or the pedals you use. If SPD pedals, must have SPD shoes. If no SPD pedals must have ties that hold your feet to the pedals. That's what makes you fall off most of the time, but also allows you to ride faster and easier. Safer too. Nothing to hold your feet down will make them come loose from pedals when going over bumps, bad.
You might also opts for carrying a back pack. If you do, have several more tubes in there and some more tools.
Hydrate. 24 oz bottle should last 5 miles, no longer. Add good mix drinks, propell or gatorade. You need a lot of sodium. Pure water won't cut it.
Get a bar end mirror. This shows drivers behind, thought body language, when you see them and when you don't see them. Helmet mirror is ok, but not as safe.
Another thing, if going SPD get mountain shoes with spikes. A) they provide traction on oily urban roads. B) Spikes provide traction on oil wet urban roads. and C) spikes look dangerous and keep drivers with bad intensions away from you. Last one is my personal observation.