I know you said pump or semi, but the Stevens 301 is super budget friendly and would be really nice to tote. They are $180 new. Without the action, the 26" barrel is still very handy. Could add a really nice Holosun for $300 and a mount from Sumtoy for $50 or so and have a sweet/simple rig. I have my boy running the 21" 870 youth. When he's hunting I can't carry cause he's only 11....and use his rig it's so nice and light and with TSS does more than my 12 ever did. Since I'm setup to load 20 gauge tss, next year when he's 12 and we both can carry a gun, that's the route I'm planning to go.
One other consideration in single shot 20 ga is the Henry. They run $470, but definitely have the old school quality vibe. I know some hate a safety on a single shot hammer, but I like the idea if I pull the hammer back and don't get a shot, can throw the safety on rather than having to let the hammer down right away. The Henry does not have a safety.
If you happen to find an 870 20 gauge and don't have to pay through the nose, the Sumtoy mount and a pistol dot is a sweet setup (see pic). The older 870s with their steel receivers do have that quality feel that very few newer shotguns have. My boy is 4 for 4 with the setup....it's been deadly.
