Currently I host via Pickaweb, £5 per month for shared hosting is not a bad plan. UK based so you are geo-targeting with the IP address if you plan to develop and optimise the website(s). They also host CPanel and Fantastico and I pay at the beginning of every month via Paypal.
I have read about site loading speed, you can GZip your site using .htaccess (simple to create) or simply ask your hosts to switch it on the server if it doesnt work. It will compress files to 70% of the current size and load faster for your visitors. You will have to contact freehost to see if they allow this.
You can host a .com domain on UK hosting and that will geo-target your rankings towards UK Google users, a .com from a US based server such as Bluehost will geo-target your rankings towards US users, etc, etc. At least this is what I have learned from experience, others may have a different view as I dont generally deal with many .com domains. I do have a couple of .com domains on UK servers and they generate 90%+ of UK visitors.
I try to keep it simple though, .uk domain from a UK based host and you are fine, as such a uk domain on 00freehost should also be okay. They say if you have at least one of the following two you should be ok:
UK based host
UK domain
Buttontop, if they allow you to purchase a keyword domain and forward it to your hosting then you shouldn't have a problem, as any link building will be towards your keyword domain, just make sure that the free hosting doesn't litter your page(s) full of adverts.
Flash etc tends to slow down a lot of web pages and people will click off your website if their web connection is super slow or the page looks spammy, which in turn will increase your
bounce rate (which is rumoured as something that Google looks at ranking wise if you use Analytics - not sure if it is true).
Try not to use a free domain (as you wont be able to sell it

), sometimes they work, sometimes they dont, but your own domain name will be much better to use and yours to own.
Terry