How can I discover which branch would best suit me?

I won't tell you which branch I think is best, what I will tell you is to think about what you'd like to do. Do you like to fix things, work in an office environment, etc? Think about what you don't like...for example, do you hate flying, are you afraid of water, or do you hate hiking? That will narrow your choices. Also, there are other ways of serving besides Army, Navy, Air Force, and Marines. Don't limit your scope. There is also the Coast Guard, National Guard/Reserves, and the Merchant Marine.

Go online and review each service- then go talk to the recruiters on the basics of each branch.

Shawnta Johnson Below is some information that provides the basics. You can go to the website for each branch for more detailed information. As stated by Maj John Bell, what are you hoping to accomplish in the military?

http://www.militaryspot.com/enlist/understanding-the-five-branches-of-the-military

https://www.thebalance.com/u-s-military [login to see]

Follow your gut...

Ask yourself the following questions -
Do I want to be a Marine? If Yes - Join the Marine Corps.
Do I want to be treated with respect and be valued for my intelligence?
If Yes - join the Air Force.
Do I want to go to sea on a ship for an extended period of time?
If Yes - join the Navy.
Do I want to rescue people from the perils of the sea and catch drug smugglers?
If Yes - join the Coast Guard.
None of the above? Join the Army.
Its that simple.

Like several others have already stated, a big factor should be what you hope to get out of serving.
To which I would add that you should also think through what you are willing to gamble. Adventure requires risk, and while the military is much safer now than in my day (when "peacetime" operations killed off the equivalent of a battalion every year), the most interesting stories you would get to tell will likely involve either someone not making it through the story with the same body configuration they had at the start, or there being a very high risk of that happening. And even if you are one of the fortunate ones who don't suffer a life-altering injury, the harsher military services will still exact a toll on your body - e.g., my knees still remind me of the years I spent in the infantry, and silence as something other than a steady ringing is just a concept for me.
Don't think I'm trying to talk you out of serving. in my mind, it's well worth doing for a multitude of reasons, but you should go into it knowing that you're running a very real risk of coming out the far side partially shredded.

Perhaps you may want to ask 'What have I to offer?'

In my opinion and experience. Most people can do anyone they wish. Basic is temporary. The JOB/MOS is what you should be aiming for. In my case, I don't think the Marines have Medics or Nurses but I could be wrong. I can't do enclosed spaces so the Navy is out. AF....they are more strict including a credit check last I heard.
Army is what is was for me. I scored well above what was needed to get a spot for Combat Medic. The MOS is most important. No matter how long you stay in or get out, that job could be hour future career. I wouldn't want a MOS I ended up disliking or hating and get all that free training and experience only to not use it after.