The hosts advertised or recomended here are good for the price, you could do a lot worse than looking at the prices there. I chose one and am happy with it.
As for moving hosts, if you have wordpress, you are lucky as you can import your blog. Not done it myself but will test it out to see if it is easy like they say.
Moving site means you will lose ratings in google if you do not redirect the pages on your own blog to the new one, you do this through .ht access file, so you’ll need to search for that.
You also need to redirect your website name or url, if you own one.
There will be other tips, such as keep your old webspace running perhaps with redirect files for a while.
I’ve had a few sites go down and was unable to redirect, the only solution is to update outside links on others sites.
Took me a few months to get back on top positions for my key words.