1 The sentence beginning "If I had to choose" will then go on to describe how I would behave if I were obliged to make this choice.
2 "If I were to choose" is the same as "If I chose", and will then go on to describe how I would behave if I made this choice.
Note that 1 and 2 are identical, except 1 mentions an obligation, 2 does not. 2 does not imply that there is no obligation - in truth the obligation could actually be the same as in 1, it simply is not mentioned, i.e. the other answerers are wrong to suggest that 2 implies you have more freedom than 1.