I would start cheap for a few reasons. 1). You are in school and probably not sure how long you are going to stick with pool and 2). The lower price point cues are going to be stiffer regardless so there is no point in buying an expensive one. 3). The stiffer and cheaper cues are good for learning on.

Any of the cues you find at the major billiards stores online will do. I would personally avoid buying one at a random non billiards store. They will have less quality in them and having your beginner cue around later for when you have moved on to a nice stick means you can turn it into an affordable break cue. Also they will likely have a crappy tip that will suck for many reasons (life span, feel, shapability, etc)

I see you are concerned about the tip diameter. Having a wider diameter will make make shooting straight easier. The narrower tips will make it easy to to put follow/draw and left/right spin on the ball. I would personally stick with what the manufacturer makes. Most of them are a 1mm or more wider than the more expensive cues and will be likely what you will want to have in the long run.

I personally used a Cuetec sneaky pete (sneaky petes are just cues with no wrap and look just like your standard house cue). The Cuetecs are pretty solid, but I would recommend something like a Poison or Players because they have a wooden shaft. You want a wood shaft. Not carbon, not fiberglass, period. Check out ozonebilliards.com you can search for cues by price point and they have legit prices.