Here is my 2 cents worth. When my daughter was certified at 15, I had her use the tables for her first 50 dives so she could understand how they worked. I figured if her computer failed in a dive she would have the knowledge to know when to come up.. We carry a computer and a depth gauge and watch so we have a back-up.
1. Go to Deep Sea Supply and for $12 you can get a wrist mount for your compass. As mentioned before, the retractable system is an entanglement hazard. Plus if it is on your wrist, you know where it is immediately.
Not sure what your average depths are but:
2. If shallow(50 - 60 feet or less), get a depth /pressure combo from $180 to 200+
3. If deeper than 60 feet,
a. Get a 2" brass and glass PG (Dive Rite or Light Monkey) for about $70 and a 21 to 24" hose for $25 to 30. Do not worry about a boot but get a $10 clip so you can clip it to your BC. If you want a longer hose, I can ship you one for the shipping cost.
b. Invest in a low cost computer for $180 or more. As previously mentioned, this will help you get a buddy who is using a computer and will also give you extra bottom time. Get a Nitrox Compatible computer in the event you get Nitrox certified. The extra cost will be minimal and you may be glad you did.
4. Dive more
Good luck and have fun.