International SMS is no big deal on many of the "unlimited" domestic talk and text plans from
the guide (I'd highly recommend staying with a GSM provider if at all possible, though). P'tel (T-Mobile), H2O Wireless (AT&T), and RedPocket GSMA (AT&T) all include "unlimited" international SMS and some form of direct dialing for international calls with either a fixed included international calling credit or unlimited international calls to UK landlines
only. The better deals on these plans start at $30/month.
In your friend's case, I'd probably recommend the H2O $30 plan (free "unlimited" UK landline calling up to 10 unique phone numbers per 30 day billing cycle with auto-disconnect after 60 minutes per call); but calls to mobile numbers will rapidly eat into the $10 international talk credit at roughly 30¢/minute, which is steep at more than twice the price of everyone else
if you fall outside the free credit range on the account, and caps you at roughly 30 minutes of UK mobile calling. Fortunately, it's prepaid, so you can't spend what's not already loaded onto the account. $20 worth of international calling credit can be had at the $40/month plan, which also tosses in an extra 500MB of high speed data and uncapped throttled data for that extra $10 worth of calling credit, but hardly seems worth it to spend $10 just to get an extra 30 minutes of UK mobile talk time.
I'd recommend going H2O due to the bigger service footprint going on AT&T. Of course, if most of the UK calling is going to be mobile number based anyway and there's a data hunger and T-Mobile coverage might work, P'tel might be the better choice at $30/month because you're going to need to work VoIP into the solution to keep the UK mobile calling cheap anyway. Plus, 500 minutes of UK landline calling at 1¢/minute as provided by P'tel still works out to 8 hours and 20 minutes of talk time.
If your friend is one of those people who thinks they need a fair chunk of data and "unlimited" talk and text anyway, this will be the simplest path with the least amount of technical adaptation... but it also means that it puts the onus on the friends and family back in the UK to pay for their end of global SMS, and/or minutes to call back if need be.
More technical solutions involving VoIP providers and data-based SMS alternatives are covered in the guide as well, but it requires at least a willingness to get a minor bit technical (which if anyone wants a smartphone, they'd better be willing to do anyway). Given the splintered fifedoms of SMS replacements and the availability of unlimited international SMS on these plans anyway, I'll briefly mention Kik and XMS (needs to be installed on both ends), and just leave it at that.
The real gain your friend will get going with an additional app on her phone for calling will be using a
LocalPhone account and the Android app. It's easy to set the outbound Caller ID to match your phone number so it's seamless on the receiving callers end for identification, UK mobile rates are 2.3¢/minute as PAYGO, or there's 200+ minute UK subscription packages starting at $3/month (1.5¢/minute or less including all mobile)... probably some of the cheapest stand alone UK mobile rates you're going to find
anywhere. Plus, the LocalPhone Android app can be set to either make calls over WiFi, 3G/4G (not recommended for data use and lag), or over a local phone number (perfect for "unlimited" calling plans). Of all the cheap international VoIP options, LocalPhone will be one of the cheapest and easiest to integrate without an absolute reliance on data to utilize, and will pair nicely with an "unlimited plan from either H2O or P'tel on an Android device.
As far as handsets go? Depends if she's willing to buy used/refurbished or not. I'd recommend something that's either already able to run Lollipop (5.x) or is well supported by
CyanogenMod (but CM is getting into needing far more technical skillsets than installing an app and entering a username and password). I'd also encourage getting a handset that has a user replaceable battery (which eliminates the Moto E/G/X series - I've not been impressed by the lifespan of the Moto E battery, and it's not user replaceable). Whatever she gets no matter what, make sure it's carrier unlocked. You can search by needs/wants/features (including removable battery)
here.
If she just wants new and doesn't care about needing to potentially replace the phone with a battery failure, the Moto E might be a good option. If she still wants new and doesn't care about Android security patching but does want a user replaceable battery, there's plenty of Blu handsets that're dirt cheap, such as the Blu Neo 4.5. Otherwise, it might be worth trying to scrounge up a good used Android flagship phone from Samsung, HTC, or LG.
Any other questions, you know where to find me.