Hello There,
There is no need for Clean install and again "Data entry" work of whole website. it means everything you have done in a years that will re-done again. in My opinion that will very-costly for you and may down your store reputation as well in both Public and Google.
What i suggest is Simple, We will copy your one store. and will setup that on New hosting, then we will Upgrade that store to Latest version and will Remove the glitches, old-skin, cache etc. This will sure safe Your time and off-course your big amount of money.
I will not suggest you Shared hosting for Magento, if you are open Good-healthy setup. I suggest bought a VPS for 12 months. i will setup your VPS in cheap prices and will available for you on Skype for future work if you satisfied with the performance and work.
Let me know your thought,
Best regards
Matli Digital