Hi, As a .php shopping cart - most hosts will be easily able to host OpenCart on a low cost shared hosting plan for you without difficulties. Good luck.
I suppose you need fast linux shared hosting with nice support, check for Hostome.com offers, they will fit your demands.
For opencart eCommerce site script any good shared hosting service is enough. you dont need any vps or dedi for that. but for a big scale like dhgate or dealextream you need to consider yourself a highend VPS or a Dedi.
Do you have any other requirements? Such as disk space/bandwidth/location/control panel, as what is listed is vague and should be supported by almost any provider.
Yes I agree more details and specs are really needed to provide you a better response. Any reliable host should be able to handle the basics of what you mention. So next specs and budget are needed to offer any other advice.
its Shopaserver.com , excellent prices, opencart along with other features. one more thing their support rocks!
I also think that hostome.com will be the best choice for your demands which you can use without any doubts.
I think Hostshore.net is best for you it met your Requirements. If you need more info don't hesitate to Contact us.