|All of the Piper Senecas except for the very oldest have the turbocharged 6-cyl TCM IO-360, which uses up cylinders if you look at it sideways. Not the best for training (!!)
The Seneca I (one) has the normally-aspirated 4 cyl angle-valve 200hp Lycoming IO-360 and is a good choice for training (ie throttle-chopping) but they're getting old, and there are only so many around.
Another neat little twin is the Piper Twin Comanche, with it's cute little Lyc IO-320's. You don't see many of them at flight schools for some reason. They got a bad name back in the 60's but no one in aviation remembers back that far anyways. Too bad, a nice, cheap little twin.
The Piper Seminole and Beech Duchees are almost identical. I really doubt anyone here is old enough to remember when they were introduced, but there were rumbles of lawsuits because of their amazing similiarity. High tail, counter-rotating 4-cyl carbureted 180hp parallel-valve Lyc 360's. These are your trainers of choice these days. Easy to as pie to fly, but dreadful single engine climb rate if you're anywhere near max gross or if it's hot/high.
Aztec is a great trainer, but a pretty expensive one, with it's big IO-540's. Easy to fly, very good single engine performance. Thick wing. Hate the f_cking hydraulics, though. Good charter machine. You might find one as dual-purpose trainer/charter.
If you go to Seneca College, and money is no object, you can train on the Baron. Like the Aztec except faster and more expensive. Why you need a fast, expensive training aircraft is beyond me, but I guess I'm not very sharp compared to a Seneca College grad