DIR Tec Diver once bubbled...
All my personal diving is DIR, and I also am an instructor, so having a computer is important, and poses no violation to DIR as long as it is in Gauge mode when used for that specific type of diving. SUUNTO is by far the best computer to get, but I agree with sticking with the Vyper or Vytec. The Vytec allows you to use multiple EANx mixtures, but if you are doing that sort of diving, you should be using gauge mode anyway, so the Vyper is the best buy. The ability to download your profiles is very important. This is how we analyze our profiles, decompression and understand what is happening on every step of the dive. As you become fully aware of this, the need for the profile deminishes and then you can go with the bottom timer such as the UWATEC.
For the Regs, Apeks are definitely the best choice, but be aware of the ATX50 with the swivel. That will wear in time, and then you will have an issue with the O-Ring. I know from experience because before I became a competent tech diver, I purchased those, and I learned the hard way. You don't want any potential failure points in your equipment, so go with the ATX 100 or ATX 200.
Now for exposure protection. If you do any type of technical diving a 6mm wetsuit is unforgivable. Get a drysuit as was already mentioned previously. There is a big misconception that a drysuit if only for cold waters. Very wrong. The drysuit is the suit of choice not only for exposure protection, but for proper buoyancy, trim, balance, safety and comfort. Even when I have surface temperatures of 40c I use my TLS350 and 200g Thinsulate, and I am not overheated in any way during the dive, and staying warm and comfortable is the key to effective decompression. Using a wetsuit only leads to problems not solutions.