How to express that you want something.

Ok, for example, let's say someone offers me coffee or tea and I want tea. Which of these ways is the best way to answer? Does it matter?

Poproszę herbatę. Proszę herbatę. Mam ochotę na herbatę. Chcę herbatę. Chciałabym herbatę.
Would you answer differently if you were in a restaurant setting as opposed to at a friend's house?

Wolałabym (wolałbym) herbatę, jeśli można.

Or "Poproszę herbatę"

Poproszę herbatę - Tea please (you use POproszę when you ask to be given something. I'd use this one or the one that Bzibzioh mentioned)

Proszę herbatę - Tea please (this one is also ok, but the previous one sounds better imo)
Mam ochotę na herbatę - I feel like drinking tea (kind of...)
Chcę herbatę - I want tea (demanding)
Chciałabym herbatę - I'd like some tea


no, these expresions can be used in both situations

In most places just say 'herbata" if you want to sound Polish. There may be some families where something else is added, but they are exceptional in my experience. In a restaurant, especially, you will sound very foreign with any polite form, but I like this and say 'poprosze'. You may find just 'herbata' a difficult cultural jump (I did), so try the more hesitant 'nie wiem, może hebatę' (I don't know, perhaps tea), which is a standard, less demanding way of asking.

'Thank you' (dziękuję) is unnecessary in restaurants and is often not said in homes either. Indeed, in restaurants, 'dziękuję' when paying the bill used to be accepted as meaning 'keep the change'. This has changed in places regularly frequented by foreigners, at least. However, apart from being aware of the latter, and only thanking when I have my change, I refuse to accept the idea of not saying 'thank you' continuously and enjoy my reputation of being extremely polite.

@sunbreak
If I may express a view, I think that "chcę herbatę" sounds rather curt, and "herbata" alone as a response to a question even more so. Politeness isn't in excess in Poland and I think it will earn you a lot of brownie points in any circumstances if you show that you have studied the social graces. ;)

My favourite is "poproszę (+acc)", but any of the ones you mentioned works. "Mam ochotę na (+acc)" is pretty indirect - it means sort of "I feel like having sth", so you probably wouldn't use it in a restaurant or bar.

"Wolał(a)bym herbatę" literally means "I'd prefer tea", if someone gives you a choice between several beverages, tea included. "Wolę herbatę" (same verb, woleć, indicative mood) makes less of an attempt at politeness, but I wouldn't call it a demand.

A superpolite (even timid-sounding) request would probably take the form of a question: "Czy mogłabym/mógłbym dostać (+acc)?", i.e. "Could I have/get...?".

Hope that helps. :)