Amazon Sword plants are heavy root feeders and do need a fertilizer for good growth. Using a liquid or root tabs is up to you, both will work.
I'll warn you though, Swords get large and can easily outgrow a 10 gallon so you may need to do some trimming of longer leaves.
You want a comprehensive fertilizer that has all the nutrients needed for plant growth. The most recommended is Flourish. It's inexpensive and will last you several years for a 10 gallon. With root tabs, they last ~2 months. A 'root tab' is just a solid chunk of fertilizer you put under your substrate near the plant. It slowly dissolves and releases nutrients into the water.
If you have the standard two screw in type hood for a 10 gallon you can use the 10W spiral CFLs. Get the daylight kind, they have a spectrum of 6500K which is good. Several companies make them, usualy GE ones are easy to find. Caution though, this will be 'moderate' light for a 10 gallon, so you'll have to cut back the light time to no more than 8 hours, but even so you could end up with algae and might need to cut that back even further. Floating plants can really help with that by cutting down the light entering the tank.