keep it simple. The work and how much your rankings will change (usually just temporary) will be dependent on what you focus to work on and how big the site is

Just do things one at a time.

• Make sure you fix all errors ASAP (images, internal links etc)
• Redirect the old urls to the new urls
• Make sure the speed of loading is the same of faster.
• Basically, just do things quickly and optimise.

Run screaming frog after and fix all the remaining errors. Youll probably see more errors in webmaster tools once your site gets recrawled but those will probably be easy fixes.

Remember, just focus and get it done ASAP and youll be fine.

I have like 8 shared servers with them.

It depends a lot on how bad the people you share with are. LOL

I have faster ones and slower ones. It really depends.

I would suggest cloud hosting with rackspace. Account is pay only for what you use

WP engine is also good as well as wiredtree.