Thank you for the advice about the ground fill - a complete, unbroken topside ground plane would be better, then?
Yup. Breaks in either layer are fine (i.e., the negative space created around a trace), as long as they are stitched around with vias. In this way, you can make even fairly complicated (though not very dense!) circuits, where traces mostly run on one layer at a time, always over ground plane (so, the fewer traces/buses crossing, the better -- trace crossings make a hole with no ground top or bottom), and the performance averages out to having two routing layers over a solid middle ground plane. It's very good, without having to buy a 4-layer board.
Like this for instance, imagine the whole board looking like this:

Here, priority is on top routing (red), with pour filling around traces. That pour is pretty sparse due to the routing on top, and it's stitched to the bottom (blue) where possible (with a preference for placing vias near trace crossings and peninsulas). Also, obviously purple is copper top and bottom, a transparent view. Meanwhile, the blue traces are short, and isolated where possible (so ground can fill between them).
Terrifically over the top for a simple linear regulator, but the strategies will benefit greatly as you move into more complicated circuits.

Well done, first layout or not. I strongly agree with Tim on making the annular ring...
Is flooby a Tim? I never noticed...

For the record, I wholeheartedly agree; I recommend pad O.D. a bit less than twice the hole I.D. Typical pad sizes:
ID OD (mils)
8 18*
12 25
20 40
30 50
35 60
40 70
60 100
80 130
etc.
*Budget fabs usually balk at holes this small.
Tim