Most of the hosting providers do not allow Ajax application on Shared hosting plans as it requires a good amount of resources. If you do not wish to choose a Dedicated server for now, I guess, VPS would be fine for you.
I’m sure an ajax will be fine on any solid provider, you just need to make sure they have a reliable and fast network or else your applications will be slow. A VPS will be a good investment if you plan to build a very fast and busy jquery/ajax application.
I can personally vouch for Beyond Hosting I have a VPS with them and get an average ping of 22ms. You can ping my domain at kelchm.com if you want to see. Best of luck
Yes, you can choose a VPS for now and upgrade if yor requirements increase in future. Also, make sure that you choose a hosting provider that informs you (via notifications etc.) when you use more resources and need an upgrade
Of course that is possible to find shared web hosting which will support you. But there are not too many web hosting companies which can offer that.
I agree with other guys in here: VPS is the best option for you now.