He’s circling the aisles of his local CVS trying to find a beard trimmer. 
While the rest of the responses in this thread have merit, the actual process by which you maintain your beard will be somewhat subjective, depending on the way your facial hair grows and the features of your face (under/overbite, flab, etc as mentioned) - but this is easily the most important piece of universally applicable beard advice ever written.
ETA: thank you for the link to beards.org, btw - fabulous stuff here.
I should add to my previous: Very important, get some women who’s opinion you trust to comment on any styles you try. You don’t care if the guys think it looks goofy, as long as the ladies like it.
Fortunately, there are a few women in my life whose opinions I trust, so this should not be an issue. I plan to buy a trimmer over the weekend. I definitely feel like it is growing unevenly, and it’s looking a little sad (in my view, anyway).
Suggestion: trim your goatee short enough to be neat, but leave it just long enough that the woman kissing you won’t get whisker burn.
BTW, the woman in you life can thank me with small, mixed bills. 
Asimovian, I’m chuckling knowingly, because I too grew a goatee after my divorce. It’s a sharp, literally in-your-face break with the past. Congratulations on finding a pro-beard girlfriend; facial hair was not to my second wife’s taste, and so my beard lives on only on my driver’s license.
My facial hair sounds much like yours. I assume you grew the goatee because that’s the only area where the hair grows in fully enough? Sometimes I long for a full beard, but it’ll never happen. My neck whiskers will grow, but I don’t want to look like this guy. Or this guy.
My few points of advice: Trim the whiskers at the sides of your mouth so that the outer edges are vertical lines, rather than curves. In my view, a rounded goatee makes my face look fatter. I also tend to think that less under-the-chin hair is better; my chin is pointy, so I shaved under my chin up to the edge of my jaw. Also, if your beard hair is as straggly as mine, I would advise keeping the edge of the chin trimmed short. Dangly, ratty whiskers drooping below my chin make me look like a vagrant.
Actually, I don’t know that my ex-wife was opposed to facial hair. I’m sure I knew at one time, but I can’t remember. I think it was mainly a non-issue just because I really wasn’t capable of or interested in trying to grow facial hair. I do know that she used to tease me pretty badly at my pseudo-mustache when I’d go more than a week without trimming the hair above my lip. My current girlfriend, however, is decidedly pro-facial hair (although she had no problem with me being clean-shaven, either).
I don’t have the slightest interest in having a full beard. I can’t even explain why. I didn’t have any interest in a goatee before, either, but that’s just because I never thought it would look good on me even if I could grow one. Maybe I’m wrong about the beard, too, but I’m going to take it one step at a time.