Hi, volunteering first would be the best option having in mind that you will be given a 3 month visa at the airport then extend it after-wards.
I was recently working with a good program in Nairobi where they had numerous projects running so I got the opportunity to do a round on them. Lived in Kenya for 6months got up to date with the culture, language and food. Basically I feel more at home in Kenya than anywhere else because I have good friends and team with me - that's what that matters.
Anyway, this organization I was working for covered all my day to day living, food, water, electricity and trips with tours were part of the company expenses, so I did not spend a lot because they understood I was a volunteer. And that's what you need.
Anyway, if you want to get in touch with the program's director/manager, his email is:
oxford510@yahoo.com and tel: +254 724 241 230, am sure he will be more than glad to give you a run down of what they do.
Have a great time in Kenya.
Jenny