I'd say start with something simple, a cheap budget model without a lot of the fancier bells and whistles.
What does that boil down to? The ?130 costing Motorola Moto E.
It ain't very fancy, mostly functional for basic smartphone usage. Software-wise for instance it has a nearly stock version of Android, with the latest 5.1 version of Android coming soon/already on it, which is quite impressive considering it being a budget model. That saves on a lot of fancy bloatware and graphical shells, leaving a clean and simple user experience.
Hardware-wise you get a surprising amount of stuff for ?130, or your regional equivalent. Is it top-of-the-bill? Hardly. But a 1.8Ghz quadcore CPU, 1GB of RAM and 8GB of internal storage with room for a microSD card is quite something for that kind of money and more than enough to run every basic smartphone app you'd need smoothly.
What helps too for a first-time smartphone user, I think, is the fact that it ain't all that big. A 4.5" screen isn't small either, but it won't swamp you like many higher-end models will. That more modest hardware suite also makes for impressive battery life for a smartphone, again especially for that kind of money; I can last around two days with modest app usage. Don't expect a superb camera either, but it does the job for the odd pic you send through WhatsApp to someone.
What do I use mine for (though I have the 2014 version)? Online banking, maps and GPS, WhatsApp, the odd bit of Netflix and Youtube, Spotify, news apps, tracking fitness progress, checking emails, audio books, you know the drill. And the Moto E does all those basic things flawlessly. The smaller size also seems to make it a little more rugged, it's also splashproof, and less prone to breaking its screen, which is nice for a clumsy oaf like me.
Do you want something a little more beefed up that's a little fancier? For around ?50 more you have the Motorola Moto G which is a little bigger, with a little bigger screen, little better hardware, camera, etc. There's hardly better budget models out there and they offer a great first-time experience.