You can find some great info at these two sites: http://www.hec.org/info/faqs/climb.htm and http://www.project-himalaya.com/info-trekking-peaks.html. The Nepal Mountaineering Association (NMA) has classified 18 peaks in Nepal as 'trekking peaks', a misleading name because all involve climbing. Ranging from 5650-6500m (18,537-21,325ft) some are, however, appropriate heights to combine within a trekking program. "Limited bureaucracy" peaks would be a better name.
You can rent everything you need in Kathmandu in the Thamel district. You can also find great info at the Kathmandu Guest House on guide services/trekking agencies that you need to sign up with. There's tons of scammers walking the streets, trust your instincts and you'll have the time of your life.
ps - Be prepared for the smog in Kathmandu by taking a dust mask or bandana(s) along. It may not bother you, but it did me.