When in doubt, start light and work up to heavy. As far as particular types of dumbbells to get, the simpler to use the better. As Meade Rubenstein pointed out, the adjustable dumbbells (dial-a-weight style) really aren't that easy to use--and the moving parts only add to the complicated nature of those weights.
The question then is fixed or adjustable?
- Fixed weights are the simplest, easiest to use dumbbells
- Fixed weights will cost more overall because you have to buy several pair
- Adjustable weights are slightly more complicated, particularly if you have to swap weights.
- Adjustable weights are less costly because you can simply buy more weights for them instead of whole dumbbells.
If you decide to go for adjustable weights (like what Meade illustrated above), I do recommend getting more than one pair of handles. That will let you have all the weights you need for your training session already set up.
In general, the more compound you can make your movements, the more you will stimulate your body to build mass. The more isolated you make your movements, the more you will shape the mass you have. For example, goblet squats will stimulate more of your body than curls. Same with dumbbell deadlifts and standing overhead press. You can do the movements unilaterally, meaning alternating sides, which will strengthen your core and stabilizing muscles at the same time you are working on other muscles.
It's best to start really light, so you can focus on technique. Do plan on regularly increasing the weights on a schedule. It takes the mystery out of "do I go up or not?", and it prevents stagnating progress because your body is used to the weight. If you can't get all your desired reps at the heavier weight, or the reps are really ugly, repeat the weight for the next cycle. The goal is to get stronger and stronger.