i'm not a pro, but since i host website on shared server i had to do some things to speed it up. I disabled all stats related modules(i use awstats logs in cpanel to track stats) , cleaned all ps_connections,ps_connections, ps_connections_source, ps_guest(if you delete all these you will lose your stats). Also every few days i delete carts not associated with orders, which seems to help a lot. Two more things that were slowing down my site were Specials Block and Catalog Price Rules, so i disabled Specials module and don't use catalog price rules.