@bamboosymphony you may try the FTP Rebellion theme for better answers, because the players there will give you far better info how to spend your limited resources and what to focus on rather than the majority of the community. No offense to anyone, just pointing the facts.
As for your current question, my answer (as a very cheap to play):
You do not need to emblem 3* even if you have no one 4* worthy of emblems yet. 3* can be used without emblems to help you complete many things in the game. Like 3* tournaments or challenge events for example. Emblems aren’t as important in these as are starting boards and tile movement for example.
Why not emblem 3*? Because fully emblemed 3* aren’t that great. They are just a bit above regular 3s. Not as powerful as 4, no. Rather, emblemed 3* are almost equivalent to 3/60 4* heroes. I can vouch for that since I have multiple heavily-emblemed 3* heroes on my side accounts - amongst them a fair number of Bane or costumed Bane, and there are several Kailanis as well.
On the other hand, a 17+ emblemed 4* hero is equal to a 5* in most cases - at least, stat-wise. And many 4* have even stronger (or faster) special abilities than some regular S1 (or other) 5*.
With a team of 4* heavily emblemed heroes you can achieve anything that a team of 5* can do, whereas at the same time your team of heavily 3* emblemed heroes won’t accomplish that much - you will barely see the difference. 4* heroes with emblems will quickly pay up for their emblem investment since with them you can complete for example Legendary challenge events. And upon completion, these give 300 emblems total.
So - play with your 3*, enjoy, amass 3* mats and 4* heroes, and when the time comes, ascend those 4*, give them emblems and start harvesting events for more emblems.
If there are other questions such as, for example, how to complete a rare or trials quest with primarily 3* heroes, always happy to help with that. Depending on your 3* hero options of course.
And one last thing - TC13 is a scam. I suggest going for TC20 instead. Of course, if you already built it, then fine, run it for now, but go for TC 20 ASAP. This is one of the first things each f2p should achieve.