If you are looking for lightning fast response but do not want to pay high prices, then an option may be some of the VMware clusters or Cloud severs that scale up and deal with high traffic times. If you have bursts of traffic during certain periods of the day or month, such as specials etc, the you pay more for resources during those periods and less when your server is idle. These can be a good solution for medium to large business requirements without paying for clustered dedicated servers. If you do a search of 'cloud hosting' you can find a range on offer.
Speed can also depend of the type of content you are serving. If you intend to stream video on demand or similar services then you would need to ensure you host has the appropriate CDN facilities to meet your needs. If high data requirements then make sure the data centre can deal with that level of traffic without blocking issues.
If your need content delivered fast to various international destinations ensure the host has clusters in the datafeed areas for the countries your are targeting. e.g. To target Australia you do not want a datacentre in the US as that route is clogged so you would need Asia-Pacific centers etc.