In terms of combos/resets whatever, try and learn L Fiber loops (this is the combo in the bnb compendium for Fortune
http://skullheart.com/index.php?threads/general-bnb-compendium.4072/). This will get you to learn how to input Fortune's Fibers which are a very important part of the character, they give good corner carry, do good damage (in retail), work for happy birthdays and are universal. For a reset you should try and do L Fiber, j.LP, j.LK, j.MP. This then lets you dash under (works vs everyone but Band and Double, and maybe Beowulf I think) for a cross up, stay same side, do an airthrow or a burst bait with jump back j.LK, j.MP (whiff) or j.LP, j.MP in the corner. This is the only reset you need to learn for now imo.
For blockstrings, try to use the string cr.LK, MK and if it was blocked then stop there and if it hits continue into a full combo. It is tempting to end your blockstrings in her rekka and go for a high/low with her slide/Gato but do not do this. The overhead (El Gato) is easily reactable and very slow and the slide is very punishable on block. If you do long blockstrings you also leave yourself open for pushblock guard cancel punishes (PBGC) which is another reason to keep your blockstrings short. If you HAVE to end a blockstring with a Rekka (perhaps you did cr.HP on block or something) then do L Rekka x1 since this is +0 (neutral) on block. Since Fortune has the joint fastest jab in the game, you will still have the advantage here vs most characters but I would still try to avoid going past cr.LK, MK. Practice hitconfirming this string in training mode with the dummy set to block random.
In neutral cr.LK is very good for catching people low due to its range and short blockstun, HP is a good button due to its size, j.LK is a good air-to-air when you are above the opponent and H Fiber is a good mobility tool (+ it is your invincible meterless reversal). Fortune's dash is great, really fast and it low profiles a bunch of stuff like Double's L Luger and Parasoul's napalm shots. When combined with her cr.LK Fortune's dash becomes something your opponent always has to keep in mind.
I wouldn't learn headless just yet since there's quite a lot to learn if you want to learn it and it's good to learn the base character first. If you do end up headless and the opponent is wailing on your head, don't try and call it back because the head will be in hitstun and you'll just leave yourself vulnerable, instead try to go in and punish them. If you want to call your head back in neutral then try calling a lockdown/horizontal assist and calling your head back. The assist will cover you while you recover your head.