If you only need a seat for other peoples cars then you don't need a travel system. Just fish the baby out of the car seat and pop her in the pram.
I would catagorise the types thus (ignoring that some are systems and some are not as systems fall into all camps).
Real Prams. These are the silvercross type sprung things Mary Poppins would like. They are good if you walk everywhere because they are comfy and have much bag carrying capacity. The are also good because they are simple to fold, of a bit large (not so large a taxi or decent car would worry, but might fill an MR2 or Corsa boot) . They can be bulky on the bus/train unless you can easily stand for your journey and they are rarely travel systems.
Pramettes. Like real prams, but a bit more modern, including that they fold smaller which can be helpful on busy trains or if your house has no space to keep a pram. These convert to puschairs for later use. Most are part of a travel system, which you may consider a bonus- not strictly needed but nice.
Pushchairs/strollers. These tend to fold up small, which is helpful for public transport, but are generally less comfy to push and have less storage than the above types. I wouldn't pick this kind for you as comfort for lots of walking is more important than convenience of folding since you will not use a car most of the time. You also need to check the age as only some are suitable from birth.
3 wheelers. You don't like them, but if you did I would say they are good for walking on grass/gravel/mud, they are stable and don't tip easily (except if you line them up wrong coming off a kerb), they tend to be solid/durable, many can have a second seat fitted for new arrivals. They are bad because they are expensive, they are not your personal choice for the prettiest and they are the worst kind to fold.
For you, I would say the choice is between a real pram and a pramette. Go to a shop that sells this stuff and have a really good play with the models on display. Ask to see how it folds and to have a go yourself, also have a go at every other major adjustment you can make, eg seat angle and handle height. Wheel it round the shop at a slow march and see if when you take big strides you kick the axle (which is a total PITA when you are rushing somewhere). Jiggle it about a bit and see if it seems to have good suspension. Ask yourself:
Is it comfortable to push?
Can I get it on the bus/train (if you use them) without a fold (tip, if it's a disabled access bus/train then they'll all go on ok)
Is it pretty? Do I actually like it?
Can I afford it?
Does it look trustworthy to me or will I worry about leaving the room if DC falls asleep in it in the hall?