I learned on Cessna 172 - various types, really liked the 172M
Did my PPL in Jan/Feb 2011, didn't fly for 18 months due to the scarcity of planes here.
So a bought a plane in New Jersey - I went for a Piper Archer II (PA28-181) - a bigger engine, faster and equally as comfortable as Cessna.
Did a couple of hours of dual in it with an instructor getting my BFR and then flew it back to Barbados - think it was easier than it would have been in a Cessna, no real reason for thinking that.
Pretty much you learn to fly and you can fly anything in the class of airplane you are certified in - with the correct type instruction - all subject to the whims of your insurance company.
Good luck with the training