Is there a specific reason to put down more cash upfront? A lot of resources mention that one of the big reasons for failure is under capitalized account.
There is only one reason why a large account is necessary. Its so that you can do it wrong over and over and over again and still have money to trade.
The fact that you say you're fairly flat is actually a very good thing. You more than likely only need to make a few tweeks. Two things I would look at is, can you squeeze more profit out of your winnings trades? And second, can you cut down on your losing trades?
The size of account necessary is actually pretty easy to determine. If you have a clue, and you keep good stats, all you need to determine is what type of drawdown your trading can encounter.
Suppose you trade the ES and you risk 2 points on each trade which is $100 per contract. Next suppose you take about 5 trades a day. If you lose all 5 trades, you're gonna be down $500. Will you lose all 5 trades? Who knows.... maybe... but only you can answer that, and even then, you never know what the future will bring. But very many trades who collect long term stats will know that for every trade, they maybe average about 2 ticks profits. This means that one trade may win 4 points, next trade loses 3 points, so 2 trades in total, 1 point profit, hence 2 ticks profit per trade. Obviously long term stats are necessary here.
The point is that when you know your trading stats in all different markets, you will know how often you can lose 5 trades in a row and be down 10 points. This is only $500. If you have a 10k account, and you trade the ES with a broker that only needs like 2-3k margin, you essentially have thousands of dollars that aren't being used, and that should never be needed for margin if your stats tell you that you will be profitable after so many trades and the worst you can expect to encounter is 5 losses in a row.
Obviously you want to have more cushion so that losing 5 trades in a row doesn't affect you at all, and you don't worry about your account size at all, but this is why I preface all this by saying its easy to figure out how much money you need if you have a clue and very good stats.
Since you're learning, 10k or even 20k might not be anywhere close to being enough. But since you say you're mostly flat, I doubt your account is money limited. I've known guys who right away trade multiple contracts. There is no different between someone trading a 10k account and 1 contract, vs. a 20k account and 2 contracts. It all just comes down to math, you win rate, expected profit from a trade, expected loss, etc.
If you have taken hundreds of trades in various market conditions, and you're never scared to take the next trade, you should have enough stats to figure out exactly how much size you can put on with whatever account you have and do this for each and every trade, no matter what happens.