Well, there are no fatal mistakes I suppose. More like deadly enemies, so make sure you avoid them
I suggest you keep an eye in Captains cost and your daily income (through treasury -> General trade report). Once you got many captains, you might want to start upgrading your fleets.
Generally,I always tell that you should start with the cheapest ships, get a lot of them and then build 1 offensive fleet (does not need to have Ships of the Line as it is too expensive and only good for the richest of players - upkeep for them is huge too).
Cheapest ships have many advantages that most seem to ignore. When we speak about a merchant ship, the #1 element is PROFIT. Yes, more expensive ships have larger cargo, but does that justify their price ? In most cases it is a NO. You can have better profit with small ships as they cost less to build and less to maintain.
Then, when you grow despicably rich, like some of the top players, then you can start upgrading them.
There have been no players to have attempted a good rush with small ships yet. Personally, I never needed to do this, as I plundered a bunch from other players. This might be even better but if you take this path, you should be ready for some trouble later.