Before getting serious about learning Mandarin I want to go to China for a few weeks to start learning the language and see if I like the country, as I would be pretty annoyed if I spent all that time learning Mandarin, just to then find out I do not enjoy China.
Anyone can recommend a good school that offers immersion, preferably a homestay and professional teachers?
I am looking for a course that will allow me to not only learn Mandarin (I guess I will not be able to get very far in a few weeks anyways), but also get me to see and experience the culture/country.

You are going to find homestays and language schools all over China. And I'm sure there are good ones all over.

But if I was going to do that for a couple weeks just to see, I'd do it in Kunming, Yunnan. Really great city. Start your search there.

Hanzimania, I have no experience with such schools, I can only speak from my experience of living in Shanghai for about four years now. Good and bad schools probably can be found anywhere in China. If I were in your shoes, I would focus on two aspects:

1. What kind of environment is most attractive to you personally? If you prefer smaller cities, simpler lifestyle, nature - then go to somewhere like Kunming, or other smaller cities in Yunnan or Sichuan (small being: compared to Shanghai, Beijing, so maybe "only" a million people). Cities like Hangzhou (near Shanghai) might be a nice compromise between "too far out" and "too big". If you are more a big city person, I would consider places like Shanghai, or Beijing (more smog...), or Guangzhou (more warm :-)). A number of overseas interns we had at our company really "fell in love" with Shanghai - they loved the big city & party lifestyle.

This is a real personal thing. You mentioned you want to find out whether you will like China. The thing is, China can be very different in different places. (Some people call Shanghai or Beijing "not real China".) If you love city life, you might find a homestay in a simple Chinese family home in Yunnan horrible. If you love nature and the simple life, you might really dislike a language course in glitzy shiny Shanghai.

2. is the immersion factor. I guess staying in a smaller, more remote place forces you to learn more in-depth. Many expats in Shanghai do not bother to learn much Chinese and can get around somehow in English. On the other hand, it is very much possible to study Chinese in Shanghai for a year, e.g. at Jiaotong Uni, and pass the HSK 5 exam - friends of mine have done it.