HappyJack, . I did something very similar to you. In addition to the suggestions you already got, I would also recommend you talk to other divers as well to get their recommandations keeping in mind that only you know what type of diving you may be contemplating in your future so you will have to weight the pros and the cons of each advice...including the one you get from the various LDS you have access to.
I also come from the Horsecollar, weight belt, J valve and single reg era. While I did buy a very good BCD when I resumed diving in 2009, it was replaced by BP/Wg systems (doubles and single/travel) a year later. Now my son uses it when we dive together. Weight belt...some folks abide by that system while others will either prefer a weight integrated approach (BCD) and/or a combination of both system (weight distribution ditchable, non ditchable, trim, etc). If you go the BP/Wg route, in all likelihood weight belt will be part of your set-up.
Computer...many models to choose from offering a wide variety of features...and cost. Here again, we all have our own preferences...some will prefer air integrated while others won't, air only vs air/nitrox/gauge modes, one button operation vs multi-buttons op, backlit vs OLED system (night diving), etc.
Regs...many good companies to choose from and a wide variety of features. Between me and my GF, we own four different brands (Sherwood SR1, Zeagle FH VI, Mares Abyss and HOG). They all perform very well and I have been blessed with great customer support from each of those companies as well as the facilities that I purchased them from. Knowing what I know now, it would just make more sense to stick with a single brand and that may come at some point in the future. As Jax mentionned, Edge/HOG seem to offer a great quality to price ratio.
Finally, may I recommend you dig into the various equipment sub-sections of Scubaboard. It represents a great wealth of information...some more opiniated than others. Just another tool to complement your fact searching process. Welcome back to the world of diving.