I'd recommend the CCFL, but doing the inverter is far easier than replacing the CCFL. I've replaced 3 or 4 CCFL's and 2-3 inverters. It's very difficult to do the CCFL, but it's more likely to be the cause of your problems based on your description. Replacing the inverter is usually easy.
Look up the price and make a choice; they're probably both cheap though. I just replaced both the backlight and the inverter in my laptop because the screen was getting dim. The backlight was $20, the inverter was $15. Replacing the inverter took 10 minutes, the backlight took 3 hours.
If you're comfortable inside of a laptop and have steady hands and some patience, you should be able to replace a CCFL bulb in a couple hours. I replaced the inverter and bulb in my old Acer. It wasn't exactly the easiest thing in the world, but it turned out fine. Make sure you remember exactly the order of everything.