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For most web pages it is not so much the number of core as it is the amount of data your transferring and how the page is laid out.
More cores can help if your site is getting tons of hits since each hit \ thread can be handled independently, but if your site is just starting up, it is hard to believe your getting so many hits that your bogging down the server even a singe core server.
Most web sites bog down because they are trying to send too much data (photos, scripts, audio) all at once and then the bottle neck is still on the recieve side. If the web page is optimized it can load the page in chunks so that the longer the person stays on the page the more material is presented (good). Some sites are configured so that nothing appear until everything finishes downloading.(bad)
Extra ram falls into the same bucket. If your site can cashe everything in ram, the server will run very fast (hard drives take forever to access as compared to ram). Take a look at your raw file size for the site and compare it to how much ram you have. Some HDD paging is OK, but if all your pages take a excessive memory, your pages are too large \ poorly designed. Thumb nails (low res) that pop up high res photos beats the heck out of a bunch of high res photos needing to load.
Bit sure if this helps you or not. The software guys or the optimization team at your provider may be helpful in getting things to ruin faster.
Once your sure the design and content is optimized then you can make a better decision on if you need more horse power to make it work.