Log Horizon is bloody brilliant.
Absolutely love the kind of main character they were going for here. In some ways reminds me of Alderamin's MC as well as Yamato from Majikoi: All three have completely different personalities but there's just this strategic side they have in common. So, yes. I love this type of MC and the shows that have them.
Liked every character, liked the plot (especially People of the Land being, well, people, too), yada yada. Interestingly, I noted various (read as: at least one) characters have accents -- It's the first time I've seen an anime with them distinctly present without at least a scene where the characters themselves take note of this.
In the meanwhile, I've also started another one, which is in many ways everything I ever wanted: Slayers;
Without really knowing where to look, I've been looking for an anime where we have characters in a fantasy/medieval land just... adventuring, I guess: doing stuff, getting in trouble, getting out of trouble, and with a focus on comedy. I got a bit of this with Inuyasha's many filler episodes, which I preferred over the actual arcs, but I like Slayer more due to the character personalities here (more suited to comedy).
Most fantasy settings I come across just seem to have a focus on the action, or on the plot, or some such thing. Slayers unashamedly feels free to add comedy wherever it feels like, and it's all the better for it. When I watch anime I may on occasion stop to think... and blurt out my own sarcastic comment at the situation or the character's actions: When the anime manages to reflect my own thoughts, then I have little choice but to revere it.
Problems with it would be the dated art. It's from 1995, which is relatively recent, and yet I have difficulty discerning much of what goes on on screen. I cannot tell if it's simply too busy for a show its age or if they just handled it badly -- I never had any problems watching anime during my childhood -- I see absolutely no reason I should have more trouble with something from the 90s than things from the 70s or 80s. To its credit, I think its mostly just a thing from the 90s, as I have always had issues putting up with art from that period.
Another issue I have is that it does have serious parts... And they are so generically typical I can't tell if it's a deadpan parody or if that was a thing back then. I'll go with the former and just keep on laughing.
Edit: In fact, the first 5 seconds of the OP tell it all. Quite enough to get me hooked. I forgot to mention the main character's voice actors, but they are both superb. The first three sentences of the OP, along with her delivery of them convinced me thoroughly.
Lina sounds like a young girl, which contrasts greatly with her power and "wisdom". Gourry sounds like the dumb bag of bricks he is. Evil guys sound stereotypically evil. Good guys sound like justice nutjobs. It's marvellous.