Demo accounts are for the purpose of learning the platform and for testing strategies and to give new traders experience.
Will it give the trader any proof of how good of a trader he is? No, only a real live account will, as there are so many other aspects coming into the picture when trading live. Just to name a few: the emotional aspect of knowing that real money is at stake, to not overtrade when making mistakes, to have risk management in place on both individual positions and on the trading account as well.
Some info can be read at RMMRobot.com about risk management which should be regarded as a #1 priority to be informed about before trading on a live account. There are so much money to be saved especially for new traders decided to go live after practicing demo trading for a few months, to be be well informed on this subject.
When it comes to the size of the trading account in a live trading environment, for a new trader I would suggest $500 because this will be enough to have proper money management without being underfunded, if the stakes are 0.01 lots or 1000 in volume per position.
" Lock in the profit and minimize the draw down "