Founder of Yellow Jacket Stun Gun iPhone Case: $100K+ raised on Indiegogo ('12) & $2M+ raised from angel investors ('13). Established multiple manufacturing relationships in Shanghai & Shenzhen China ('13 & '14). Launched two separate smartphone accessories at CES ('14 & '15). Passionate about helping other hardware entrepeneurs.
While Catherine does a great job of explaining your options below (from a business POV) I believe that it would help you and us if you were able to provide a bit more background on what space/area your theory is involved in & what your intentions are. There are many fields of science such as life sciences, behavioral sciences, physics, etc.
To say that you have a theory that you haven't shared with anyone and presumably haven't tested a bunch of times would probably not go over too well within the higher echelons of the scientific community. As an entrepreneur, I constantly tell other people that ideas (or "theories") don't mean much, but rather what you do with them does.
In very simple terms, if you'd like to be the first person to be documented as having this theory then there are things you can do like publish a book/article or even record a video/video blog and email it to yourself or your attorney. Doing this should time stamp your introduction of this information to the known world.
If you want to get real deep then keep reading...
Apparently, there is an interesting "theory" about theories themselves called "The Underdetermination of Scientific Theory" which basically says that a scientific theory can only be disproven and not proven: https://www.quora.com/Why-can-a-scientific-theory-only-be-disproven-and-not-proven
The same user on Quora goes on to say, "In practice, this distinction often turns out to be largely semantic. Theories are not proven, but "accepted", with the notion that we might retract that acceptance in the face of new data. But that's under-playing the fact that a good theory has been tested many, many, many times, and it's quibbling to act is if there's a serious chance that it's incorrect (especially if you're not actively working on a better theory that also explains just how the old theory managed to survive so long)."
Lee is pretty much spot on here. You can do what it take to compete, try to join them or find something else and move quickly. And don't worry, there is always something else.
I'm not totally sure that you have to know the correct class in order to file a patent. I was under the assumption that it was the patent examiners job to ultimately determine this. With that said, I'm sure it's quite important to know what class you'll end up in and this should help you complete a patent search of other competitors in the same class. Also, if you have a budget for IP, a thorough patent search done by a reputable IP firm will bring back information on any potentially overlapping patents and you can check and see which class these patents are in and work backwards from there. Also, I'm pretty sure your product could belong to more than one class.
My main question would be this: When you say "like Monster.com" what exactly are you referring to? What is your secret sauce?
As Lee mentioned, if there is a specific filtering/matching algorithm that you've developed that you feel fits the following categories (requirements for a patent) then the answer is YES, you should file for a utility patent.
1) New and useful (No one else has Known about or used this process or algorithm in the US & there are NO patents on this anywhere in the world)
2) Utility (actually useful in real life or a very solid theoretical foundation for being useful)
3) Novel (Unique, authentic idea - See #1)
4) Non-obvious (This is the hardest obstacle to get through. Simply put, your idea can't just be the combination of 2 other patented Ideas. Previous patents are called "prior art" and your idea will be compared against prior art to ensure there was a substantial difference in your invention versus previous inventions. Patent examiners will also look at the commercial marketplace.
5) You Haven't publicly disclosed your idea
If you don't have a secret sauce and you're creating a website that duplicates someone else's algorithm/process then you may be infringing on someone else's patent & you should ask yourself why you're going into business in the first place.
To keep it short, def go for the licensing route if you're not comfortable getting into the manufacturing business. I've done it and it's tough. You should be able to shop potential licensors by going to the local hardware store and seeing the main brands on the shelf & going after them. You will need a good sell sheet. Listen to this podcast, bud, it will help: http://www.smartpassiveincome.com/how-to-get-paid-for-your-ideas/