Now to get this thread back on topic.
Assuming your folks get a dynamic WAN IP, you'll need a router whose firmware supports DDNS (most do), or an endpoint running on the network which is always connected and running a DDNS updater, and then an active account with one of the corresponding supported providers. This will allow you to forward yourparents.ddnsprovider.com to their public WAN IP at the given moment for remote admin by you.
For scheduled reboots, I find that typically only 10-20% of consumer boxes offer this stock, so if you want that out-of-the box, you may have to step up to a "prosumer" class device, or be comfortable with running an open-source firmware like Tomato or OpenWRT.
In terms of stability, that's rarer still, but I find much better better odds in choosing models that have been on-market for long enough to generate a solid consensus. Both for the stock firmware and any others.
For a recommendation, I've run countless $35 Asus RT-N12s on AdvancedTomato for SOHO clients with simple topology needs (like your parents) and routinely get year+ uptimes with never a phone call about anything acting up. So it's definitely doable without buying an overpriced betaware erector set.
Assuming your folks get a dynamic WAN IP, you'll need a router whose firmware supports DDNS (most do), or an endpoint running on the network which is always connected and running a DDNS updater, and then an active account with one of the corresponding supported providers. This will allow you to forward yourparents.ddnsprovider.com to their public WAN IP at the given moment for remote admin by you.
For scheduled reboots, I find that typically only 10-20% of consumer boxes offer this stock, so if you want that out-of-the box, you may have to step up to a "prosumer" class device, or be comfortable with running an open-source firmware like Tomato or OpenWRT.
In terms of stability, that's rarer still, but I find much better better odds in choosing models that have been on-market for long enough to generate a solid consensus. Both for the stock firmware and any others.
For a recommendation, I've run countless $35 Asus RT-N12s on AdvancedTomato for SOHO clients with simple topology needs (like your parents) and routinely get year+ uptimes with never a phone call about anything acting up. So it's definitely doable without buying an overpriced betaware erector set.