From Kathmandu, you basically have two choices, either the Annapurna Circuit or else the Everest Trek. Of course there are more choices, but they are uncommon or else tough. Along those two main trekking routes, you should find inns and teahouses for lodging, if that is your plan.
In either case, you want to avoid bad weather. The monsoon season runs during the middle of the summer, so you want to go either before that or after that, and not during the monsoons. September might be good.
On my first trek to Everest Base Camp, we started around the end of September, maybe the 29th. We were told that it would be at least a couple of weeks after the end of the monsoon season, so it should be good. Well, we got rained on every day for the first week. I was prepared to rig up my boots and socks with plastic bags (between sock layers), and I was used to enough rainy walking that the mud did not upset me greatly. Some trekkers were demoralized after several days of rain. Also, during that wet time, the leaches come out. Once it gets dry enough, or if you get high enough where it is cold at night, then you won't have the little suckers anymore.
There are some places that will want to do business in the local currency, rupees. Other places want to do business in greenbacks. I recommend having lots of each. Do not count on plastic.
On my first trek there, we were walking for a week just to get up around Lukla. By the second trek there, we could just fly to Lukla, so that shortened the walking a lot. The problem is that some people try to fly into Lukla, then hustle up the hill to Namche, and that sets them up nicely for high altitude problems.
Take plenty of personal medications. You can't expect to find a reliable doctor or pharmacy up there. There are some doctors, but you can't expect to find them when you need them. Specifically, take water treatment and also the meds necessary if the water treatment doesn't work (like Immodium). Take a broad spectrum GI antibiotic, and probably a prescription-strength painkiller, just in case.