I was there near the tail end of spring and caught just the tiniest edge of monsoon season. I'm afraid I don't have much to add except that in addition to the predictable amount of rain in the lowlands, the other inconvenience is leeches.
I only encountered one but in contrast to the stereotypical American leech, the one I saw in Nepal was quite active, relatively far from a water source, and looked something like a small, energetic inchworm. I was told that they can stretch themselves to be quite narrow and can infiltrate boot eyelets. I was also warned that if refilling from a stream or creek to filter/strain/examine the water before drinking as there is a small but rather inconvenient chance that you could end up a nasal leech infestation.
You may want to do your own research regarding the latter two observations and consider a clothing/footwear system that is leech resistant.
It's definitely possible to rent/buy most of your gear in Kathmandu with the understanding that it will be cheaper and lesser quality. There is a thriving trade in black market versions of outdoor gear. Some of it quite imaginative. In fact, I wish I had picked up a version of a Patagonia down sweater which had a tuck away nylon hood sewn into the collar. I thought Kathmandu had some half decent down products. And lots of ok generic nylon trekking clothes (shirts, pants, hats, etc).
However, I wouldn't buy any goretex or membrane based waterproof jackets with any expectations of there being an actual membrane. There was also a dearth of quick drying underwear and other performance baselayers for sale.
Hope that helps. Let me know if there are any other questions I may be able to answer. Otherwise, have a great trip!
ps. Besides the wet, the other reason people tend to avoid the monsoon season is that it tends to be rather hazy, obscuring the views.
edit: to add note about haze.