Quite casual, but more to the point it respects your time. There's very few time sinks or grinds (and the few that there are, namely Ascended gear and Legendary weapons, are optional and/or will be alleviated by the expansion). There's no gear treadmill either; once you're in exotic-tier equipment you're pretty much done, with progression based on cosmetics and fun (that is, they're anyways adding something different and new to do).
There is a LFG system (no raids, all of the large fights are open world), but if you're in the GAF guild you can usually get a group for just about anything really quick. Even if you're in Europe, I'd advise rolling on a North American server (most players who do report little to no latency, your millage may vary) so you can play with us.
And yes, the initial purchase is all you need, there is an expansion off in the future but there's no date or price for it yet. There's also an in-game cash shop, but it's all cosmetic or convenience items, so its up to you if you want to spend more (you can also convert gold to the cash shop currency and never spend a dime).
Edit: No subscription fee either, of course.