Any brand of normal dies should work in any normal press type. Most dies are 7/8" thread. There are some speciality ones and older rare stuff but 98% of them are compatable.
Along with press, manual, dies, scale, measure etc I would also recommend you have a way to measure cases to .001" ($30 digital calipre) and a way to trim cases right from the beginning. Another thing is the Lee scale does work but is not as nice and friendly as more expensive scales like the Ohaus/RCBS 5-0-5 balance beam scale.
No matter what brand of gear you get buy a tin of Redding's Imperial Sizing Die Wax for case lube. You may use other types but will find jobs where this works better/best.
With the Lee kit you get a trimmer and just need a case length gauge for each calibre. Other brands use lathe type trimmers that may or may not come with the parts for various calibres. I would also recommend you start with normal FL (full length) sizing dies before you worry about neck sizing etc.
An example list might be
Lyman 49th Reloading Manual
Lee 50th Kit
Lee #3 shellholder (RCBS dies don't come with the thing that holds the base of case in the press)
Lee Case Length Gauge for 6.5x55
RCBS 6.5x55 FL dies
Digital Calipre from Home Depot