New Guest - I don't know what that means in terms of rates.
Rack Rate = the rate that shows on a hotel's website if you are just a member of the general public and not looking at a price that is discounted either under a publicly available offer code (like ones found in the Discounts thread here, or on a hotel's own website), or a player's club marketing offer. So this is the highest possible rate.
Comp Value = The hotel and casino are separate operating units. When you book a marketing offer from a casino, the casino operation pays the hotel operation for the room, typically at a discount of 30% or more to the rack rate. The amount the casino pays the hotel for the room is the comp value of the room. The casino needs to recoup that amount (and a lot more, to be profitable) from you through your play.
Example: You get an offer from a 3 night comped stay in a "Deluxe ABC" room. You go to the hotels website and without entering any discount codes, you see that the typical rate per night is $100. When you book the casino offer, the casino is probably going to pay between $60 - $70 a night for that room, and they'll be looking for you to generate between 3x - 4x that amount in theoretical win (for them) via gambling.
Other rates - Most hotels offer discounts to everybody at any given time, via offers on their websites and through third party travel sites. It's pretty hard to actually end up paying rack rate unless you are not aware there are discounts.