Your average speed depends on a lot of things: traffic lights, hills, terrain, and the level of effort/discomfort you're willing to put out.

I'd recommend that you not worry at all about hitting any particular average speed. Just focus on safety, logistics and getting a good workout. Give your body time to get acclimated to the bike, pedaling, and the cardio load. A 36 mile RT daily is a stiff commute by any standard, so you'll want to ease into it.

Bike selection is a huge topic, but I would say that if you're a novice, your taste will change so don't commit too much money. Instead get something that is comfortable and reward yourself with what you really want as you drop the weight.