Question: > 
> *I want to go home.*
> 
> 
> 

Here the word *to* belongs to what part of speech?

Answer: 
> 
> *I want to go home.*
> 
> 
> 

I'd say that infinitival "to" belongs to the word category (POS) 'subordinator', and its function is that of 'marker', a meaningless element that simply introduces the VP.

It functions in much the same way as the indisputable subordinators "that", as in *I know that she lent him the money"* and "whether", as in *I'm unsure whether it will rain.*

Note that infinitival "to" derives historically from the preposition "to" (notice the strong similarity between *I went **to** the doctor* and *I went **to** see the doctor*) but long ago lost its prepositional properties.
'To' in 'to kick' is, according to Wikipedia, an infinitival particle. The infinitive 'to kick' without 'to' so just 'kick' is called the bare infinitive, whilst 'to kick' is called the full infinitive.