Online VS Offline features

Would it be possible to set up private matches with friends who also have the game?

I always prefer online. With a live contender it's always more interesting to play )))

Optional multiplayer with some "Career", "Exbition" and "Training" modes, just to try out a few diferent moves or just enjoy a match, you know?

I would definitely recommend prioritizing an offline mode. I'd also recommend a story mode or at least the ability to make a story mode. This game might become a nice platform to create a whole new class of catfight materials (outside the videos, literature, and arts)

Ideally for the finished product, both would be great, but I suggest single player first, as multiplayer comes with a whole host of issues such as servers for people to connect to to play against each other, maintaining those, and what would happen if the game was online only but the servers were taken offline years down the road because the cost of maintaining them was too much for the income the game would be bringing in.

This might go long, fair warning in advance in case it does. As a former game tester and designer for a now defunct company, I can tell you that I believe the base game needs to be addressed first before you move into either creating net-code or AI for multi or single player respectively. The issue with single player is providing the correct level of challenge from how the AI responds to all the possible things that could happen. Online, in my opinion (i reserve the right to be wrong), has more pitfalls that need to be addressed. How will you handle rage-quitters for example? If there is a ping discrepancy, how does the code handle it so that the match is fair for both players? Is there going to be some manner of ranking system where there is a champion and challengers? The list of things that needs to be accounted for is rather large on both sides of the coin here. Long story short, developing the meat and potatoes of the game is far more important than developing the final touches of the net-code or AI structure that enable multi or single player respectively.

I think both should be possiblre. So I choosed both.

How about offline at first with PvP later. I'm picking the last one.

It's a difficult choice but I voted the last one. I think one of the major weaknesses of the online PvP model is finding the right opponent at the right time. Unless there are thousands of players connecting at the same time it could be frustrating connecting and being unable to find a person to play with. So I would rather stick with a fair amount of playable bots with different difficult levels.