The battleforce is better than most, but if you want a competitive-ish army that can mostly keep up with 5th edition codices, your options are limited.
The Dire Avengers, Wave Serpent and (for smaller games, which I'm assuming you'll be starting out with) Warwalker are quite solid. Make sure to give the warwalker scatterlasers. I'd certainly NEVER mix and match the weapons, even if the sprues DO rather handicap you.
A capable eldar force is going to consider of Dire Avengers (who are either shooty or, my personal preference, a minimum-sized squad that just serves to "upgrade" their transport to be scoring) in Wave Serpents, Fire Dragons in Wave Serpents, Fire Prisms (either 2+ or none at all) and Falcons who either keep farseers safe or who port an extra squad of minimum-squad sized DA around and a farseer.
As far as weapons go, for small points games Missile Launchers are solid, and shuriken cannons (underslung on every vehicle, in smaller games TL on the Fire Dragon transports), scatterlasers and brightlances are key. The brightlances are a tad overcosted pointswise, but in big games (1750 starts to really need then, at 1850 you pretty much HAVE to have them) they become a neccesity. If you have a number of WS turrets (you can buy 'em sepperate) and just keep 'em detachable, or if you follow the guides here at HO and elsewhere and magnatise the guns you can swap stuff around easily. S6 firepower is our key strength. Well, that and the fact that fire dragons are fucking amazing.
For HQs... well, Farseers are good and Eldrad is awesome once you have the points to spare.
It seems harsh, and it means ditching most of the codex, but as an old codex that saw it's more popular choices nerfed when the newest dex came out, we're looking at a monobuild. If you want to buy other stuff for fun then have at it, but if you want your money to go farther, that's how I'd do it. Ask away if you have any questions about the whys, etc. I know that money is limited for everyone and models aren't cheap, so I'd rather not see someone buy stuff and then realize that it doesn't keep up.
Her(?) name may be slightly inapropriate, but she just needs love! And I just need to eat your face!
I'm probably going to follow my usual Eldar tactic of driving around the table "circling and screaming 'I don't give a fuck' with my windows down and system up" and avoiding anything that looks scary.