Goggles - I've seen a bunch of Bolle (I've always liked the brand) goggles for $15-$30 that look pretty nice. Except the fact that they all have what appears to be a pinkish hue to the lens. What's the general consensus on that?
Googles are a fairly personal preference item. Different goggles fit different faces differently. Go to a good ski shop in Avon when you get to BC - Suggest Christie Sports right on the main drag in town. They have a lot of googles to choose from. For example, the goggles that fit me well don't fit my son. My daughters helmet interferes with my goggles if she tries them so hers are different. That's the other guidance - while helmets and goggles tend to work well together, you need to try them to make sure they compatible with each other and your face.
The pinkish hue helps with contrast and getting the blue light out. You get a lot of blue at high altitude and during cloudy conditions. When there isn't bright sunlight, you can get "flat light" conditions. You'll totally understand the first afternoon you ski in the mountains and you get either overcast or in a heavy shaded area. You'll lose all the detail in front of you and the color helps to bring some of that back.
Helmets - checking out some rental places, they seem to be about $10 a day. So covering a 5 day trip for 4 people, that's going to add up to a bunch. I've found some relatively cheap ($40 give or take?) on STP and with a coupon, that could end up being less than the rental. Except my wife is not too find of traveling with 4 helmets and then storing them back in FL for a year or two when we might go skiing again. Should we just rent? I hate to throw away $ like that, but I see her point.
Don't ski without a helmet. Your co-pay at the neurologist will be more than the cost of the helmet in many cases. Don't go cheap or with bad fit either. Rent a good one or buy a good one but don't go without. I'm a ski patroller and can tell you first hand it's a big deal (besides having one literally save my son's life last year). It's not a panacea but wearing helmets has cut head injuries something like 60% or so at ski areas (not exactly sure of the numbers but it's very significant). As far as helmets go, again it depends on the fit, size and shape of your head. It's pretty hard to get it right without trying it on first.
Ski/boot rental - we're starting off and ending in Denver, and one friend told us to rent the equipment there instead of at the resort location. I did check Christy's last nite and they appear to be right - its significantly cheaper to rent in Denver and just keep it for the whole time (I think) plus they have the kids discount. You guys tend to agree?
Unless you know how ski boots are supposed to fit, I'd rather have the ability to have a local place to go and fix problems. Boots that don't fit right can be a huge problem. If you rented them in Denver and there is no outlet up in Avon, you'd be stuck. Otherwise, you could go back to the local shop in Avon and they could help you out and fix the problem. I'd guess since the questions you ask indicate that you haven't really done this before, you probably are not going to be quite sure of what a proper fit is so there is probably a good chance to have a problem.
Hope that helps. What I'd do is call ahead to ski shops in either Avon or Vail and get set up with them before you go. Then when you get there, you'll be all set. Good choices would be Christie Mountain Sports, and (I think) Beaver Creek Sports. Both have multiple and accessible locations. Beaver Creek Sports is in the Westin at the base of the gondola and also has a shop (IIRC, someone correct me) up at the Beaver Creek Village on the mountain. Christie Sports is right downtown in Avon and is very accessible and has a good selection of equipment, clothing and accessories. My bet is that most places will be somewhat overstocked given the slow start to the season so there might be some good deals to be had on things like goggles etc...
There are many local shops and I'm sure others can make suggestions as well.
As for lessons, Vail and BC have a great ski school. Just go up there (or call ahead) and ask them. They'll give you good advice and probably have a program that will meet what you need. We've used them when our kids were little and found them to be more than helpful.
We own property at BC and are there all the time. You'll have a blast. Don't try and figure it all out on your own, make sure you contact the ski school and ski shops ahead of time. That way you won't go tromping around while wearing ski boots trying to figure it all out.