The equipment that you want to have with a good start up kit will include:
6.5 gal bucket or carboy for primary
5 gal carboy for secondary
bottling bucket
siphon equipment (hoses and auto siphon)
bottling equipment (bottling wand and capper)
brushes (for carboys and bottles)
hydrometer
thermometer
no-rinse cleanser
On top of that you'll want:
test jar or thief
5 gal kettle (optimally stainless, but just about any kettle will do for starting out)
a solid ingredient kit (I always opt for beginners to stay away from internet recipes, rely on published sources and your lhbs for help there)
bottles (brand new is optimal, but you can save cash by cleaning and reusing crown cap bottles, it just requires more work)
I highly recommend getting a kit with some sort of secondary option (carboy or better bottle) over just using buckets for the whole process. Carboys and better bottles reduce the amount of air being exchanged with your beer. Plus it allows for your beer to clear better on top of reducing diacytel and acetaldehyde in your finished product, making a much better beer in the end.