My wife, 12 year old son, and I are new to diving. We are looking to begin our equipment collection and our instructor recommended beginning with the regulator. Any advice on nice starter regs for us
I would not begin with regulators. I'd begin with excellent exposure protection for the water temps you would like to dive in. Then, depending on where that is, think about a BC option, but make sure you try both backplate/wing systems and soft BCs in actual diving situations before your decide. Then I'd think about a wrist computer if your diving is on charters or liveaboards, and finally a regulator.
The wetsuit (or drysuit) will make the most immediate impact on your diving enjoyment, and it's important that you get something that fits really well. Of course I'm assuming you already have mask and fins, if not, get those too. Get simple fins, don't get sucked into the hype. There is ZERO reason to spend more than $100 on fins IMO, especially for gimmicks. They just have to fit well.
The BC type and fit also has a really big impact on diving comfort, but it's a bit more complicated. Check out the gazillion threads on backplate/wing systems vs jacket-style BCs and you'll get an idea. It's impossible to get an accurate assessment of these systems unless you actually dive with them; trying on in the dive shop tells you almost nothing about their performance in the water.
If you're diving on charters or liveaboards, with multiple dives per day and multi-level profiles, like in the caribbean, a simple wrist computer will make your life easier and improve your bottom time substantially. You can rent them, but they're relatively cheap to buy, easy to transport, and you want to be familiar with their use. There's another advantage for computers with new divers; they all have audible alarms for ascent rate violations. While this can certainly be an annoyance to other divers, it can really help with those first few dives in blue water open ocean. Many new divers don't realize they're heading for the surface until it's too late to stop.
Regulators are sold with all sorts of hype; don't listen to it. I could use any regulator I want and choose 25 year old+ regs that cost considerably less than $100/stage. All regulators more-or-less do the same thing. I have a hobby of working on them, and as such am very interested in great performing regs, but I don't fool myself into thinking that it makes much difference on the dive. As long as you have something that is in good working order and is made by one of the big, long standing companies, it will work great. You can rent for a while until you get a better idea of what will work best for you. It's important to get something that you can get serviced easily, and if you're diving in extremely cold water, (drysuit temps!) then you should get a sealed regulator that is more freeze-resistant.
Best of luck, welcome to the forum and diving!