The kids are trying to exert control over a life that is going to change, and they are understandably nervous about this new arrangement. Even if they are excited in some ways, it's an adjustment.
No, they don't get to pick the house. There are way too many variables. Don't take them with you when you house-hunt. It's okay (and a good idea) to discuss with them the types of things adults review and consider when buying a house: price, taxes, location, insurance, maintenance, etc. Then they'll all want new furniture and a bedroom of their own, plus a pool and a private bathroom - what kid wouldn't? You let them know you've heard their requests and wishes, you can get them to put things in priority order so you know their values, but then you make it very clear up front that nobody's getting everything on their list. It's also an adjustment for you and your fiancé, and the kids have to respect that too.
You've also got private school tuition to consider (whether or not it's paid for by someone else), combined food bills, activity fees for kids in public school, uniforms and everything else. If you want all the kids to go to school together in order to bond, then 2 kids will be making a big adjustment and 2 kids will not (if they stay in the same school). So extra consideration has to go to his kids. But if your kids learn that you feel their school has higher standards and the new step-siblings are going to "have it easier", that's a recipe for conflict. So figure out how to nip that in the bud!
His kids would have to have separate rooms - the boy gets his own room because he's the only boy, and it has to be the smallest room in the house. The 17 year old probably only has 1-2 years left in the house, so she could get her own room with the understanding that 1 of the 2 younger girls will get that room when the 17 year old graduates. Or, your 2 girls could room together since they know each other a whole lot better, and the younger one will get her own room when the oldest graduates. Compensate them in some way - those who share a room get the largest room and maybe get a little more of a decorating budget. There are, for example, screens that help divide space so each kid has some privacy. Get some decorating magazines from the library or put them to work researching it themselves - but everything has to be budget-friendly.
Another way to go is small bedrooms and a large family room or media room, or a basement that can be a hang-out for kids and friends. They don't spend a lot of time in their bedrooms anyway. So everyone makes compromises.
You COULD involve the kids in furnishing a great room or a game room, and give them some freedom there. Not complete freedom, mind you - but some say in it. It can be a bonding experience and help them feel that this new home belongs to all of them equally. And they can all learn to shop via Craigslist or yard sales and flea markets.
Finally, take some time to maybe get some family counseling on how to blend these 2 groups, and learn strategies to let each family still have its own identity (him with his kids, you with yours). If you and your fiancé plan to get married soon, then you'll be involving the kids in wedding plans as well. It's a lot. I have 2 stepdaughters and we did not involve them in the house selection but they were part of the wedding (we all walked down the aisle together, my husband wrote special vows about family being about chemistry and not just biology, and so on).
Good luck! Life's a journey even if there are bumps in the road!