Most of my knowledge is in the forex arena, for what it's worth.
It is possible to become a day trader for a trading company. The advantage is that you can work with a large account, which offers the potential for half-decent returns if your trading is up to scratch. The main disadvantage starting out is that you are only paid via commisions.
Thus, you will most likely need to have enough money stashed away to support yourself while you learn the markets and techniques that the firm trades and uses.
For example, I had an interview with
Lynx Captial Partners as they were looking to open a new office near to where I live. They only trade NYSE stocks, and my interviewer said that it generally takes between 7-12 months to become profitable enough to consider it a decent wage.
I remember seeing a similar recruitment drive by
FXCM, for new traders to join their New York office. I don't see a link on their website anymore, so they might or might not still be looking.
If you want to be trained on how to trade by someone then working for a trading company is probably the best route to go.
If you have enough money to get by for 7-12 months with needing any additional income, and you have a passion for trading, then it seems to me to make more sense to just do-it-yourself, as long as you have enough extra capital to make a go of it. Your enthusiasm and motivation will get you a long way. I would still recommend you find a mentor as this was the single biggest factor in my own journey to becoming a half decent trader.
Never trade money you need to pay the mortgage or have for your day-to-day expenses, as that sort of pressure will only adversely affect your trading.
Larger banks and other financial institutions might offer some sort of base salary to begin with while they train you, but it normally always boils down to commision pay in the end. And who can blame them. If you can't make money for them, then there's not much point in you getting money from them.
It also helps to show that you can actually trade too. If you have always been demo trading then I recommend at least opening a small live account, and place very small, low geared trades. There is a powerful difference between demo trading and live trading. It has to be experienced to be appreciated.
Never look at your starting capital as being a down payment on getting some experience. It's still real money, and you should look to preserve your capital at all costs!
Rob Booker makes this point very well in this video:
http://www.fxcmexpo.com/video/RobBookerQT7512K.swf
You should also find lots of useful info on the Trade2Win board, as it even has a section dedicated to posts on Trading for a Firm:
Trade2Win Boards - Trading for a Firm
After having reviewed all my options, I have decided to go down the path of trying to make it on my own.
It can't hurt to compile a list of companies that are currently looking for entry-level traders and find out what they're looking for to see it even begins to match your expectations.