I've been contacted a few times by players looking for ideas on how to get started.
As currently implemented, burners are challenging. They're intentionally tuned that way by CCP, and in general I'm pretty okay with that. But that also means that they're the territory of expensive faction ships and fits and perfect skills. Attention to detail helps during your fight, but the dps in vs. dps out math is harsh. You need to kill the bad guy before your tank breaks, and the minimum requirements for both tank and dps are set pretty high.
First, if you are good with a blaster boat, many of the single burners can be done with a Daredevil. (I am not good with a blaster boat, hence my variety of ship types). This necks down the number of hulls you need to buy and the skills you need to train tremendously. However, it's an expensive way to experiment if things don't go well!
But if you are interested, see this forum post and key in on the phrase Unified Daredevil.
So, second, run with some friends. Nobody says you gotta solo these things. Many mission runners fly solo, and I get that, but here's a chance to break the trend. But with 2 or 3 VERY cheap Mortar Team Kestrels on the field, 3 of the 4 Team Burners should be do-able.
Third, run with a link ship if you can. Being in a Fleet has its own passive boosts, and having a command ship sitting off grid running 5 links makes a big difference, especially for those (Worm) where speed is key (the afterburner/mwd link is a big deal). Link ships will take the edge off, require less overheating (and the possibility of burning out modules), and cause you to take less damage. So yes, run with some training wheels if you must.
Lastly, choose your battles. Personally, I avoided the Blood Raider Cruor (single burner) for quite awhile because my projectile skills were lacking.
So skip the ones you're not ready for, and embrace the ones that match your skills.
Also keep in mind that not all burners are created equal. This is my current order of difficulty.
1. (Easiest) - Blood Raider Cruor w/ Jaguar
2. Serpentis Daredevil w/ Hawk
3. Angel Dramiel w/ Vengeance
4. Guristas Worm w/ Daredevil
5. (Hardest) - Sansha Succubus w/ Retribution
I listed my ship types because the hull you fight with will dictate the difficulty. The Blood Raider Cruor has a really nasty NOS that will drain your cap. The Jaguar fit I use is a passive tank shield ship that needs near zero cap to run.
With a link ship running, I can set up the fight and go make a sandwich. Easy. However, my attempts at the Cruor in a Daredevil, which requires cap injection and range management met with disaster.
The hardest kills for me right now are the Worm (because it requires some good mwd/tackling button pushing to get right as well as managing cap injection) and the Sansha Succubus (needs near perfect skills, expensive faction webs, and a lot of overheat management).
Anyway, that's my thoughts for the moment. There's no magic bullet (sorry) and no substitute for training time and flying expensive hulls. But there are ways to reduce your exposure and dip your toes into the deep end of the frigate PVE pool.