I have used the FL-505's from this source and they seem fairly stiff, but I did not use unusually long pieces. If the weapon is not excessively laden (heavy with tape and foam), it should be fine.
If you have any worry about it, that site also has FL-524, which is slightly thicker, and I am confident it would be rigid enough to be usable, as long as you find foam of the appropriate size to cover it with.
I would not use a .505 core for anything past 38" or so, especially if you haven't been making a bunch of these.
How long is your target prop?
If you are making something with a thin profile, you can get away with FL-610 as long as 66-72". (I don't know if you can get an 84" FL-610. Pretty sure that's not allowed in FI anyway so whatever.)
If you're doing something oddly complex, or you don't know how to build out a handle with PVC or foam, or you are in general making some kind of greatmaul or halberd like object, you may want to go with FL-745.
I would not personally ever bother with carbon fiber core. I don't consider the difference in weight to be worth the cost. We're not building a kite here. Pultruded fiberglass rods are totally legit for this purpose.
If the prices for those cores at goodwinds.com are making you wince, you can try tap-plastics.com. However, be aware that some of the crafty folks around here have been screwed over by tap-plastics.com recently. (for those of you who know him I am talking about Brenz and he ended up deciding to ditch tap and go back to goodwinds) I've never been screwed by them but I buy somewhat less crap than Brenz does.
OK, in that case I'd go with FL-610. I looked at the stuff on goodwinds and on tap-plastics earlier today; goodwinds is pricier, but not quite by enough to care, especially if you can get a batch of 6 cores and share them with friends.
FL-610 is really good for boffer staves. If you have friends in fantasy larps, I'd say check with them and see if they'll go in on an order with you before you shell out for your cores, just to save on shipping.