You should get GSM phones. Generally, Atnt and verizon iphones are GSM, but you will need to call your service providers to unlock your phones for international use.

Then, when you get to Nepal you can get your relatives to buy a sim card from Ncell. Then you can buy recharge cards to add money to your account. From this money, be sure to deposit money for 3G web use, if you don't put in the money for 3G web use, Ncell will deduct Rs 6 every time you use web from your phone. You should purchase 100 MB at once for about Rs 140 - you do it by proportioning the recharge money to the web use by dialing some code like *90099# or something, and it should last you for a while depending upon your use. Also, generally it's a good idea to turn off cellular data from your phone settings so that your phone does not keep on auto updating your emails, FB, and other applications automatically because that could drain your data plan.

For transits, some airports have free wifi or you get 30 minutes free wifi. Also there will be free stalls where they have computers with internet access for free, where you can charge your phones/ipads/laptops. In Delhi, they had a weird system where you have to enter your phone number and they would text you the log info for free 30 minutes. I had to put my US verizon phone on Roaming to get the access code. Some charges may apply if you have to do this!

I am not sure about internet to go devices, but most of the airports do have some kind of internet setup you can use without having to pay. If worst comes to worst you can always use your credit card to purchase wifi. Any kind of device such as iphone, android, ipad or tablets and/or laptops would work. Personally, I think ipads are nice and give worry free performance, but be careful of concrete floors succeptible of breaking the ipad screen as it happened to me, but thankfully they could repalce the screen in bishal bajaar for Rs 5000 so it wasn't too bad.

Good luck with the travels!