I was choosing the pram/travel system earlier in the year and these are a few things I learnt/considered:
WHEELS
Solid or air: Air tyres make for a softer ride, but can puncture, so you might need to carry a puncture repair kit with you. Replacing the tubes can get expensive and annoying if it happens a lot. Also, for a softer ride, check there's suspension on the wheels.
Three or four: Four is a bit more stable, three is more manoeuvrable.
Big or small: Big wheels are more easily manoeuvrable and forgiving on various terrains, but small make the pram a lot more portable, especially on public transport.
Locked or mobile: Do the front wheels turn or are they locked in position? A lot of systems give the option for both, you flip a switch and they can be locked or not depending on what terrain you're tackling. Locked is better for gravel and such, having the ability to turn is more manoeuvrable.
Removable: Some systems make the wheels removable, which can be good if you have a small car but want a big system. However imagine standing in the rain and having to faff about removing/storing muddy wheels... Is that a problem or not?
Brakes: Some have a little foot pedal, some have a bar going across the whole of the back. I found having a bar annoying, as I couldn't then use my foot to help lift the pram up steep curbs. You definitely want to make sure that you feel confident the brakes will hold!
FRAME
Weight: How heavy is the frame? It's finding a good balance between something you and your partner can handle/carry, and something that feels satisfactorily sturdy.
Size: Big can be more comfortable for the baby and last a bit longer, but will be a problem when using public transport or small shops. Small will store easier and fit better in the boot of a car.
SEAT UNITS
Car Seat: Some of them will clip onto frames with or without special adapters, so you can transfer baby direct from the car without waking them. However, small babies shouldn't spend more than two hours at a time in a car seat as they get all squished up.
For car seats, you can just attach them into the car as they are by using the belts. However, you can also get docking stations that stay in the car which you clip the seat to - much quicker and easier if you're going to be removing the seat a lot. (i.e. Putting baby in/removing baby from the car seat while in the house, rather than standing in the rain next to the car.) Some of the docks are secured by the belts, some can be ISOFixed if your car has the option.
Carry Cot: On the bulky side, but good for a newborn and will clip on and off the frame if you're visiting friends or such and want to leave the baby asleep without bringing the whole travel system inside. Some can also be used overnight as a moses baskets, others can clip into the car across two seats to make a more comfortable ride for a small baby, so useful for multitasking. The car ones are also good if you think you'll be making car journeys of more than 2 hours. However, the carry cot probably won't last more than 6 months at the longest.
Seat: The ability to lay it completely flat is necessary if you want to put a newborn in it. Also worth considering is whether it will face backwards as well as forwards, there's a school of thought that says younger children prefer to see Mum/Dad by facing backwards. Also, some seat units can be left in place when the pram is folded down, others need removing.
HANDLES
Two handles or one long bar? Also, if you and your partner are different heights, the handle needs to be easily adjustable and comfortable for you both to use.
STORAGE
Is the size of the shopping basket important? Do you want pockets on the side of the hood to store extra little bits and pieces? It's worth considering whether you'll be hanging the changing bag over the handles, or dropping it into the shopping basket.
APPEARANCE
Is having a specific colour or trendy appearance important? Is being able to have lots of options to add accessories important?
Some prams have more options than others. For example plastic rain covers that are designed specifically to fit that model, parasols and changing bags that match the colour exactly, etc.
CLEANING
How easy is it to remove and replace all the covers when the baby throws up all over them? Can the covers be shoved in the washing machine? How long will they take to dry? Most of them are relatively easy to remove and can be machine washed, but it's worth checking!
COMPANY
Is the company who makes the pram good and reputable? What is the warranty like? How are their safety records? Is getting hold of them to replace parts easy or difficult? There's no point importing your perfect pram from the other side of the world if it becomes a nightmare if something breaks.
COST
From my experience, it is mostly a case of 'Get what you pay for' with cost. Picking up a really cheap system can backfire as it falls apart after a few weeks. On the other hand paying over the odds can be a waste if you end up barely using it. In some cases you will end up paying a bit more for the brand... Bugaboo springs to mind.
For a new system with just the basic frame and seat unit you're probably looking between about £100-£300ish depending on what you go for. However adding on extras like Car Seats and Rain Covers can push the cost up significantly.
I think my entire system (I went with Britax B-Smart 4) ended up around £600 in total, which was the frame, seat unit, car carrycot, car seat, car seat dock, foot muff and rain covers. Other brands I looked at were iCandy and Bugaboo.
Getting second hand is an option and can save a fair amount of money. However, there's always a risk that it might have undeclared defects, come from a home with pets/smokers and/or not be in warranty so replacement parts will cost. Depends whether you're willing to take the risk and save the money.
Best thing I can suggest is get yourself to a variety of parenting stores and spend a few happy hours playing with their systems! Take them to pieces, race them around the store, etc. You soon get a feel for what is important to you.
I hope that's helpful!