Looking to purchase a trailer, vehicle advice needed first

Hello, my wife and I recently decided that when our boys get a little older that we would like to purchase a trailer or 5th wheel for regular weekend camping trips. I've spent the last few weeks doing research so that I can be as educated as possible before making our move sometime next year.

Our situation is a little unique in that we have a 20 month old and two 3 month olds. As you might expect, our vehicle choices are limited as we need to account for 3 car seats (we recently had to purchase a minivan because of this requirement). I don't think I am going too far out on a limb by saying that I am limiting our options to extended cabs and SUV's. My thinking is that because of this limitation I should probably identify the vehicles that will fit my family and then try to find corresponding trailers. Is this a wise wise assumption?

Here is our tentative plan:

1) Find a truck/SUV with high miles and a low price (under 10k). This will be a third vehicle for us so I don't want to break the bank here (and ideally I don't want to pay for collision on my insurance). If it breaks I'll just go buy a new one. I've done some research and it seems as though there are several SUV's out there that can tow roughly 9,000 lbs in their base model. I know that I would be future proofing myself by purchasing a truck but in the short term I do have the car seat requirement. Part of the reason I want to take my time with this is that I might get lucky and find an extended cab that is in my price range. Then again, long trips might be more comfortable in an SUV but I'd probably be limiting myself to certain trailers if I did go the SUV route. I don't expect to be doing much driving in the hills as our area (Western New York) is rather flat.

2) Find a trailer. Ideally we'd like to get something close to 30' and it looks like there are several used trailers that run between 6,000 and 7,000 lbs. I'd love to get something a little bigger but I realize that this might not be practical.

So that is my story. Once again, I am getting my ducks in a row so that I can take my time and find something that is right for us. Any advice that you might have would be greatly appreciated!