its never a bad idea to get a medical before you start but after that you have to decide what you mean by "fitness", do you think being able to run a marathon is "fitness" or being able to do 100 press ups is "fitness" ?
once youve decided that you need a benchmark to start from so before you start set yourslef a test, and that will depend on what you want to achieve but as a starter you could try
1500 metre run timed
then 2 minutes of press ups, 2 mins sit ups, and 2 mins burpees and record how many you did
the 15 20 metre runs timed
this is a pretty good all round test but you can adapt it any way you wish.
once youve done this you can do the exercises necessary! its not rocket science to reduce your running times and increase the exercises you can do...dont worry about being too scientific in the early stages
to improve on your running RUN
to improve your press ups DO PRESS UPS! simple
then repeat your test after a month!
youll be amazed at the improvement
obviously if you can find someone to do it with it'll be better providing they are as (or more) motivated as you are...but at the end of the day its down to you..
good luck!
jeff