I would recommand that you better look at dedicated option. While you can use a shared SQL DB (To save SQL server license costs). This will give you better flexibility, reliability and scalability. Since you expect transactions to go double in one year, it could be earlier also. It is better that you opt for a solid solution now, so you don’t have to rush in future.
Princing difference is very little actually, if you see performance and reliability.
VPS would be enough initially for sure, but long term dedicated would be best, IMO. It may be best to start with what is needed long term if they are willing to budget for that.