Overpaying on a tracker or other type of mortgage?

Hi

Not sure if this is the best forum to ask which is the best option for me of a tracker / fixed / variable rate mortgage BUT do they all allow you to make overpayments every month?

My two year fixed rate is almost up and I'm anxious to get my mortgage down.
It's currently 380K with 33 years to go.

Would a tracker with overpayments sound like a good option?
And do overpayments come directly off the capital?
And would it be a good idea to put a lump sum off as I remortgage?

Thanks folks!
PW

Would a tracker with overpayments sound like a good option? YES
And do overpayments come directly off the capital? YES IF U SPECIFY SAME
And would it be a good idea to put a lump sum off as I remortgage? YES

The last question needs more details - do you have a pension, what amount would you be paying off - do you have rainyday cash reserves, are you likely to need monies in the near term etc etc

Paddy