Personally, I haven't set up a store in the Czech Republic yet, but I have set up stores in other European countries like France, and there weren't really any complications compared to settting up a US store. Concerning payment gateways, here are the major payment gateways suppoted in your contry.
If you need any help setting your store, just let me know. As an official Shopify Partner, I'd be glad to set up a free Skype consultation to go over all your needs and to provide my services in order to get you an optimal store. Here's my e-mail: michael82605 (at) gmail (dot) com.
use 2checkout.com. I just got accepted by it, I also live in Czech Republic. Note that, your website should look like professional business, and your emails should be in professional language. Despite the fact that they hate dropshipping model, they sometimes accept it whenever they trust your business. It was the case with mine