So, I am newbie in filmmaking.
I have a MiniDV camera - JVC GR-DX37E.
My first question is about software: what program to use after shooting?

Well Andrew,
thats a very bland question. First off, you have to ask yourself, what type of movies am I going to be making? How much time will I spend on this? How much money do I want to spend on this?

Money is the most essential aspect. Professional editing software can cost as much as $15,000. Or, you can use iMovie or Windows Movie Maker(which come free with most new computers) until learn more. Above that is what most amaetur filmmakers use, Adobe Premiere, Vegas, Avid Express, Final Cut, etc. Most of those software packages range from $450 to $1200.

Hey, I am from Ukraine!
I can buy Adobe Premiere for less than 3$
So, i don`t need much money to give it on software.
So, i can spend more money on production of a short film.
Of course, i will buy a license soon... But at first time i just want to learn how to use this stuff.
I need a programm for filmmakers with a beginner lever.
But i don`t need Movie Maker.

i vote for a class feild trip to the Ukraine. It's shopping time!!!!

We have a very big CD and book market where you can buy everything...
But what about programs? I`ve already looked at Vegas and Premiere. Premiere is much better for me.

It must be pirated software - so just don't explain how the market works please

Most Windows users seem to prefer Avid over Premiere... but I'm not sure.

If you're working on a microbudget, try Pinnacle Studio. It's cheap (like $80) and fully upgradable once you get the money. Personally, I like Pinnacle because it's easy and it works. The company addresses every major issue and sends free upgrades to fix them so it's a time and user tested program. I recommend it.

80$ for Ukraine - big money.
But Premiere seemes to be simple for me.
Are there such programs for Linux?

The best I know of for Linux is Cinelerra, but I've yet to use it. It has issues, but it's the closest comparable for that platform.

Definately find away to acquire Premier Pro, if you don't already have it, Pro is like umpteen times better than the non-pro line ups.