There are opinions all over the map on this topic. What's best for you will depend on your current skiing, how you learn best and your finances. With the information you've given, taking a group lesson at Brighton sounds like the best choice.
I don't personally know anyone at Brighton. I do know that Alta and Snowbird have some outstanding pros on staff. Our own Bear Lonnie
is at Alta!
In general, taking a private is always best for people with more money than time. Most (but not all) people learn more, faster in a private. Choosing your pro for your private is a big plus for some folks (if you have the knowledge to choose one that's a good fit for you - either by recommendation or past experience). A private is also better for people who have learning challenges, or are ready for a breakthrough, or have an opportunity to be with a really special pro. Many skiers with basic issues (aka a lot to learn) can get more for their money in a group lesson, but it is always a crap shoot whether you get a good pro and/or a good group. At upper levels, your odds of getting a good pro for your group lesson are better. Since groups are so much cheaper, you can afford to roll the dice more often with groups than with privates. Another thing to consider is that the best pros at larger resorts are often booked well in advance.
An option you may want to consider is taking a lesson at your local resort in Vegas. They should be even less expensive and it's easier to work on stuff on small mountains vs "wasting valuable vacation time learning" (ooh - I'm going to catch a load of crap for that one).