Welcome!
Arduino. There have been complaints about the Sainsmart products. Arduino's are available in the US,
at RadioShack even. Mouser.com also carries them, not far to ship (Texas) to you. $4.99 residential delivery. Good prices on replacement chips when you smoke one.
http://www.mouser.com/Search/Refine.aspx?Keyword=arduino
http://www.mouser.com/ProductDetail/Atmel/ATMEGA328P-PU/?qs=%2Fha2pyFadujcrAcowhVCzj0vtgCenYitTBfrdeSNJnmn1EI7EVhhFw%3D%3D
Sainsmart: "The biggest warehouse is in China, where most of the products are shipped from."
So that's not going to be fast.
The IDE is a good choice for a beginner programmer. Work thru the tutorials in the Learning section of the website, poke around in the Playground.
www.dipmicro.com (NIagara Falls, Canada, but ships quickly via USPS)
and www.taydaelectronics.com (Bangkok, Thailand, but ships locally from Colorado pretty quick too)
are good sources for thruhole components, not so many choices presented that one feels totally overwhelmed by what's available.