As a hobbyist (with an EEE background) I seldom have an order that is large enough to make the mouser/digikey shipping costs palatable. If I need something quick (forgot a particular component) then Amazon often works great, although the 'free' shipping means everything is going to be at least $10. If you area business then Mouser etc are the place to go, but you'll also have a business account with friendlier credit and shipping terms.
For hobbyists it is really difficult to beat Aliexpress. Long shipping times but you can order a whole slew of components and stock up on things you might want to try out in the future. Yes you have to pick through potential counterfeits and you may get the odd broken board/component but I'm not sure that is very different from mouser, digikey, spark fun etc?