I bought a cheap $100 approx stroller to take to the UK with me. It was nothing special but geez it took a beating and stood up well to the challenge. You can take your stroller to the door of the plane with you so it is not to likely to get damaged. As I was travelling alone with my daughter the stroller was laden with backpacks between travel spots. The stroller lied down almost flat and sat up stright. I took it on some serious off roading (to used to my magnificent 3 wheeler) and it only stuffed up the frame slightly. It is kinda abit lopsided with the steering now but completely useable.
I can only recomend measuring the length of the pram when collapsed. Mine is quite long and will not sit flat in the boot of my Barina. So if you are hiring a car or planing to use it in the future keep that in mind.
I don't think I would recomend a wet weather cover for baby unless you have heaps of room to lug it around with you. I took a disposable all in one raincoat which I just put her in and rolled back up again when not needed.
Also something light. There where lots of stairs in sightseeing areas in London so I needed to be able to carry the pram, Akina and a backpack up flights of stairs. Always ask if they have a lift or to leave the pram somewhere if there are heaps of stairs. I learnt to pick the pram and her up in one rather than take her out, unload, collapse and reverse.
I have no idea of the brand but it wasn't anything special it was along the lines of Mothers choice (the company who makes this has 3 brand name products) and Akina was 12 months when we travelled.