First of all, you should register your game so we know what version you're playing, as different versions have different compete chance rules.
When you're in a trade league, you can't compete with each others, so if the CoT is already filled with your trade members, you have to wait till someone outside to kick a slot away. The benefit is that you can using your Trade League master's compete chance, or yours if yours is higher.
Trade leagues aside, here's the first problem for you. If you are going toward free trade, instead of just sending your merchants to your own CoT, send them to every CoT in range that have a higher than 65% compete chance. You can't free trade without kicking the asses of other CoTs!
Second problem for you, owning a CoT does not increase your chance to compete if you're free trade. In fact it decreases it. If you're planning on owning all the CoT though, you should go toward full mercantilism instead because you get a much higher chance to keep your merchants in place.
The problem with Free Trade is that you're sacrificing 90% local CoT compete chance for 20% global compete chance and 10% trade efficiency. (this is the DW values, different expansions have different numbers)
That means if you want stable merchant chance in your own CoT as a Free Trade nation, you have to also change your slider toward Plutocracy, get the trade efficiency and compete chance NI to have a shot at keeping your own merchant.
Then comes the problem for most monarch countries: You start out highly aristocracy and mercantilism, and you have domestic slider restriction at 0 of aristocracy/plutocracy until you turn into an empire.
In my opinion, you're better off going full mercantilism if you plan on expanding your empire further to prevent the constant merchant replacements in your CoT.
With that said, only join trade leagues if you wish to compete in foreign CoT. Though their usefulness will stop when you have the power to conquer and own every CoT for yourself and form a monopoly with 6 merchants. Either way, stay full mercantilism and profit off the trade master's compete chance on foreign CoT isn't a terrible idea, but you'll still have to constantly waste your ducat on replacing your merchants..
Edit: oh yeah, until you have a sizable nation, or good amount of tech and buildings, every nation needs to mint to have the money to place merchants, build units, maintain army/navy, build buildings etc. That means national bank, master of mint to mint for income without penalty are almost always a must early game. Throw in war tax during war, and reducing army/navy maintenance during peace time, you should have a much more steady income for your various needs.
