Hi Amy
It should not be a problem in June - when it rains it gets it over and done with. June is a fairly popular month to visit Kenya.
Kilimanjaro is in Tanzania. You can get a bus from Nairobi to Arusha - takes about 6 hours. You can combine a Kilimanjaro climb with a safari - to Serengeti and Ngorongoro. Kilimanjaro is climbed all year round.
However, leaving a message as such on forum boards will attract lots of small time operators to respond offering their services - maybe even posing as previous clients.
If you are going to climb Kilimanjaro you want to be sure you go with a reputable company, that uses good qualified guides, provides quality camping equipment, provides good food and does not "cut corners". Cheapest is not always best
All tour operators marketing their itineraries through our Travel Center at this web page
http://www.africaguide.com/travel/
are fully registered and reputable companies. You can read feedback from previous travellers.
To view all the Kilimanjaro itineraries visit this web page
http://www.africaguide.com/travel/view.php?cmd=9&page=1&specials=5
all these itineraries can be customised to include a Safari.
I climbed Kilimanjaro last October - have a look at some of the photo's here
http://www.africaguide.com/travelog/EA_2004.htm
and our safari photographs here
http://www.africaguide.com/travelog/EA_2004_1.htm
Feel free to use the Contact Us Link at the top of this page or click the "SEND ME AN EMAIL" link below, if you have any specific questions