Michel had the right ideas.

Drop bar = road components

Straight bar = mtb components

That's the way they work. You just can't put STI levers on a staight bar; nor can you put mtb levers on a drop bar. It's not mix and match. OK you can physically mount them, but you can't operate them. Plus the brake levers are designed to work with specific types of brakes - mtb levers with v-brakes or cantilevers, road levers with caliper brakes. There are some cantis designed to work with road levers for cyclocross, such as Avid Shorties. Frame also dictates type of brakes - road frames have caliper mounts, mtb frames have posts for v-brake/canti.

Now you can use a 9sp mtb rear der such as LX, XT, XTR with Ultegra or DA if you want to be able to use cogs up to 34T on the back

Is your ride mostly decent roads? Do you want to ride with drop bars? Set up a sturdy road bike with road components.

So your choice of components is based on the frame and bar type you decide on. As I said you can mix some things road levers with mtb rear der, but NOT road levers with mtb FRONT der.

It is hard to list every possible combination that is compatible or incompatible. If you have specific ideas, ask. Feel free to PM or email me. I promise not to tell you any idea is stupid.

A very good choice for commuting is a cyclocross frame. Basically a sturdy road type frame but with posts for mounting v-brakes or cantis. Designed to be used with drop bar and road components. You can put on the Avid Shorties or other similar brakes designed for use with road levers, a cyclocross crankset which has a smaller bolt circle so you can use smaller chainrings. Use an XT rear der and Ultegra or DA front der depending on which levers you choose. You will have a sturdy commuter that will ride almost like a road bike, but able to stand up to some off road use. Check out the Surly CrossCheck, a very reasonably priced cyclocross frame.

Oh, an important consideration. If you don't have a nice secure, protected place to store your bike at work I wouldn't build up a nice bike. If you have to chain the bike to a rack outside get a good old 10-speed at a garage sale. Clean and grease the bb/hub/headset bearings, clean and lube moving parts on levers, brakes, ders, replace the cables and housing, probably some new tires and tubes, and you will have a good riding, servicable commuter for under 100 bucks. If you are an average size you should be able to find a decent-fitting bike.
Hope this helps.
Regards,
Raymond