There is no "right" answer here. I take it this is your first trip to Vegas? If it's 3 buddies going to gamble, drink, party etc I see no reason to waste money on 3 rooms, you won't be in them much. You didn't mention if you are going over a weekend or only during the week, there is a big price difference between Friday/Saturday and Sun/Thurs. You'll get a wide range of opinions on where to stay. One person will rave about a hotel, another will have had a bad experience and tell you to never stay there. You can get a reasonably priced room with a good location. Somewhere like Harrahs' or Bally's or Luxor, etc... Not a dump, not high end. Based on your post you're willing to spend up to $450 a night total so if you do want to splurge a bit there are some great deals on suites that will easily accomodate 3 people. Or even somewhere like the Rio which has a standard room (suite) of 600 sq feet.
I would suggest going online and joining the rewards clubs, such as TotalRewards and Mlife. even though you've never played there you can get good email offers.
I would recommend several options for booking a hotel. Go directly to the hotel website, try the travel sites if you are familiar with them. Call the hotel directly. And call a travel agent, often they have some good specials you can't get anywhere else. If you check rate online, log in under your rewards ID first (if you joined), the rates you get will almost always be better.
Don't overlook downtown, even if you prefer to stay on the strip (understandable if this is your first trip), you still want to go downtown. Lots of fun, cheap casinos and somewhat of an "old" Vegas feel.
