I second NameCheap. The sign up process is fairly straightforward and free of un-needed upsells, but may be confusing to people unfamiliar with basic internet jargon/terms. However, I wonder how "easy" sign up needs to be if the hypothetical mother in question is savvy enough to know that she wants to purchase a domain name, rather than say, register her vanity URL on Facebook and call it a day.

Thanks for the tip, I'll definitely keep it in mind. The upsells are a bit troubling to me, though. Mom doesn't need SSL and certainly no website creation tools or hosting (WordPress all the way). I'd like to recommend a registrar that really just focuses on domains.