I only have a trailer - burley solo. It's awesome! I picked it over a seat because it gives my son more protection from the elements. He can also have stuff in it to entertain him, snacks and a drink, so it seemed more suitable for the longer rides we wanted to do with him.
I picked the model I chose because of its weight (obviously the lighter the better), ease to pack flat/ store and internal space (it has bowed out sides so gives more shoulder space for an older child and has good storage space behind the seat).
He's been in it since 5 months - i have an additional attachment called a 'snuggler' which turns the seat into more of a hammock. All rides have been over 90 minutes in length. He absolutely loves it (he's now 12 months).
The trailer has handled well off road (rough gravelly cycle paths, canal towpaths and disused railway lines) and it's never tipped... despite inadvertently being cornered on one wheel. It also handles very well on the road.
The hitch is very simple to use (uses the quick release).
We've towed using a carbon cyclo cross bike, touring bike and our race bikes. Race bikes aren't ideal because of the gearing. You'd just use what you are comfy on (the hybrid?). It's best to go for the lightest bike you have as it'll make towing a bit less tiring. It's also worth going for the one with the lowest gears (unless you live somewhere super flat).
If I was doing the regular short commuter trips you plan to do I'd probably look at a seat for that... and keep the trailer for the longer rides. My reasoning there would be that the seat would be attached to my bike and ready to go, whereas I'd have to unfold the trailer and hitch it.
There's a great site called two wheeling tots, they have a Facebook group too. I found both really good sources of advice - there's a lot of scaremongering online about taking babies cycling.