The 3 most common treks in Nepal are:

• Everest Base Camp
• Annapurna Base Camp (a.k.a. ABC)
• Gousaikunda (the Frozen Lakes)

We did the Gousaikunda and there are a lot of options so it can take anywhere from 4-8 days depending on the route (if you are going up and then down or going all the way around).

The ABC (Annapurna Base Camp) can take anywhere between 11-21 days since you dictate the pace at which you do the trek. There are a lot of villages to stop so you can do 2 hours of walk a day or 8. It's up to you.

I haven't done the Everest Base Camp but it is suppose to be a bit hard. 

The best advice I can give you is to get to Kathmandu and go to Swissa (it's in the Thamel). All Israelis go there. You can consult with them about the time and various treks as well as get an update on the weather.

Also, talk to some of the people there in Beit Chabad and in Swissa (there will probably be a lot of Israelis there). 

The weather is very critical in most of these treks (even for safety reasons, not just because of the view) so its very important to get good information on that and have a good detailed map of the trek.

In general most of these treks are very configurable and depends on the time you have and how fit you are (if you are not that fit, consider getting a porter).