The method of jailbreaking depends on the device in question. Remember that not all iOS and/or device combinations are jailbreakable. If it's a signal dropping issue and a poor battery life issue, we'd recommend confronting the Genius Bar to see what's wrong with the device, especially if the device is still under warranty. Otherwise, it might be a software problem that's later fixed with a new iOS update, in which case we'll need more information about the device, such as carrier, current iOS, which iPhone in particular, etc.
There's no real "basic" jailbreak to be honest. You can lightly tweak a device and consider that basic, but in terms of a beginners-intermediate-advanced-expert kind of tier for an actual jailbreak, that doesn't really exist to my knowledge. But, if you're referring to what specific tweaks that you want on the device for your wife to enjoy the device a little more, definitely check out the front page of Cydia for recommended/popular apps/tweaks. You can start simple with SBSettings and Winterboard, which hasn't really changed that much from their initial releases all that long ago. F.lux is a nice tweak as well, which changes the display's "tint" so not to strain the eyes at night or at day, and the list goes on. I'd say ask her what she'd like to see "new" to her device and try to incorporate that through Cydia tweaks/apps.
