Your 603 Experian score would be your middle score, because it's between your 599 Equifax & 647 TransUnion score.
Where did you get your credit scores though? From a mortgage loan officer, or a website you came across?
Mortgage lenders use FICO scores - as a consumer, other than from a mortgage loan officer, you can only get your FICO score from Equifax & TransUnion from http://www.myfico.com as Experian no longer allows consumers to get their actual FICO score. If you are at a website where you can get all 3 scores, you can be pretty certain that they are not FICO scores but a newer scoring system called Vantage credit scores. Vantage credit scores use a lot of the same information to calculate your score, but it gives different "weight" to different parts of your credit profile, so the credit scores are not the same as your FICO scores. I am not sure why Experian no longer allows consumers to get their FICO score from them, I could only speculate that because consumers are not their clients, creditors are, so that may have played into their decision to prevent consumers from getting it. Whatever the reason, at least you can still get your Equifax & TransUnion FICO scores from that website.
The "mid score" is quite literally the middle score of three. In your case that's 603, with 599 being low score and 647 the high score.
I'm not sure from your question the source of your credit score. If this score was not provided by a Mortgage Lender using the Fair Isaac system, then the credit score is highly suspect. I have seen variations of as much as 100 points in either direction in scores between Fair Isaac or FICO scores (the system we use in finance) compared to the "free credit report" scores on TV. So, if you didn't get your score from a Mortgage Lender, then reach out to your local Mortgage Banker and get properly prequalified.
Credit score TRUTH from the source, Fair Isaac: http://www.myfico.com/
If your FICO score is actually 603, then it is unlikely you would qualify for mortgage financing at this time.