Good for you.
Eventing is an awesome sport.
Fitness is very important. I personally bike between 4-10 miles 3 days a week.
Core strength is vital as nothing ever happens on a flat manacured surface, yoga is also good.
But certainly,yard work,stall cleaning,house chores,or looking after kids can be just as physical.
If you can find a Trainer that is certified through the US Eventing association [ICP]that would be great, if not try to find one that Events. Hate to come down on anybody, but a lot of Hunter barns have found there is money to be made and try and teach Eventing. You really need to be careful as you can get hurt. It's a huge difference in riding style.
The levels are really easy. To start out go to a Combined Test [CT] that is just your Dressage and Show Jumping. You can start @ walk/trot Dressage[USDF Dressage tests [
http://www.usdf.org/docs/tests/2008_..._movements.pdf -only good for walk/trot,the others are USEA] with 18" fences. Many areas also have unrecognised Horse Trials [HT] they run all 3 phases. Usually they start with a canter test and 2". And to find those look to your local Eventing organization. On the computer type in the state your in state [ex. Maryland Combined Training assoc.]
From there you can move up to recognised, you will need to become a member of the USEA. It has the lowest division called Beginner Novice, canter test and 2'9" jumps. Moving up the divisions your Dressage gets more technical and your jumps higher but only 3" per division. The jumping isn't so much about height as it is about the technical aspects of straightness,accuracy,balance,timing....
Even though it is winter try and find 1 to watch. If your in the south, they are all over the place.
This is the offical web page it should help some.
USEA - United States Eventing Association (Eventing, Combined Training, Three Day Event, Horse Triathlon, Equestrian Sport)
Good Luck