On computer, buy the best that your budget will allow. This will help you get longevity out of it as your diving progresses beyond the level you are currently at. Make sure it handles nitrox, AI is a really nice feature. I like larger numbers on the display. Perdix is a popular choice, I went with Suunto vyper Novo with transmitter for less that just the perdix costs. The perdix will do more but it is well beyond what I will need anytime soon. The Scubapro G2 is a solid option too.
Regs depend on what features you want. I use an aqualung legend supreme, have an atomic b2 on my pony and Apex for sidemount. All have pros and cons. I like the legend for the cold water diving I do, I like the extended service time on the atomic (2 years between service saves a ton especially on my pony reg) and the Apex breathe like a dream.
As for what to do now, dive dive dive. The biggest leaps in my confidence and skills early on occurred when I could dive everyday for a long period straight through. A trip to Cozumel for a week or 2 of 2-5 dives a day would do wonders for your skill level and confidence. The repetitive diving allows you to improve on at least 1 skill a day, then build upon that the next dive while the previous improvement still being fresh. I between those trips be sure to suffer through the sub part local dives to keep your skills fresh. Put a bunch of dives under your belt before you do rescue, this will allow the diving parts to be second nature so that you can focus on the skills you gain during the class. Nitrox is a great class before any trip that has repetitive dives. Get your own computer before you take the class though. And finally, have fun