Is it a bad idea to have a different homepage and a different "first-page"
I remember in the days of Macromedia Flash, it was a somewhat popular to have a splash page, which took up the entire screen. It would traditionally contain the main links and advertising regions. Web designers confused the splash page with the homepage and clicking on their logo would return you to this animated page. Once you enter the website when you click on the logo you do not return to this splash page and not the homepage. Luckerly Wikipedia did not do the same mistake.
Furthermore links to this splash page internally seriously affected user experience; imagine every time you click on the logo to be directed to the heavy flash based introduction, a little annoying to say the least. Search engine optimization was also on the down as the homepage contained little to no text information about the company, instead it would contain an animated introduction created to draw existing users, but lacked in drawing in new users as it did not have the proper SEO principles to get noticed via the search engines.
Back to the original question and aiming at UX, what would the users expect when they go to your website, what would they expect to see?
The answer is your website in full, a splash page to select a country or language is acceptable, as many global websites take this approach, however, an introduction page to promote products is not going to work in your best interest, particularly as users went quick relevant information. If there is a very important notice you can easily have a pop-up appearing on your website on first load.
Your design looks good for a homepage and a first page, I would keep this as the homepage. Furthermore the home link should always be on the website, it should not appear only within deep links. This again affects user experience.
Everything has to make sense, otherwise you'd either annoy your user or loose them completely.