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Actually this is a very interesting topic to discuss. Mys v1.4.0 will have more powerful features, but it will most likely use more resource than Mys v1.3.x. I cannot really say how much it is compared to the old script, but if your server runs Mys v1.3.x fast you should be just fine. If Mys v1.3.x runs slowly on your site, chances are your server will not be good enough for Mys v1.4.0.

For a beginner's new site, a shared host should be sufficient. You can live with hosts like HostGator, Bluehost and so on. If you get tens or hundreds of users online every minute, you may need a VPS server. I have a dedicated server with WebhostingBuzz , I personally like it and will recommend it to others, its customer service is superb. But honestly I cannot speak for their shared hosting services since I am using dedicated server(and apparently, webhosts are much nicer to people who pay $100+ a month than $10 a month). Also note that some webhosts work well for certain people, you may just have to try them out to see which one suits you the best.