I've never thought of lever action rifles as having a complexity worth the gains, I prefer going down to the bolt action or up to a semi-auto. Which, for that matter, can be fairly simple for lighter rounds, in fact, you have to add complexity to keep many (all??) of the designs from being full auto.
Parts count of a bolt action is a bit smaller, but that's potentially deceptive. I'm pretty sure the tolerances are actually much tighter with a bolt action. If that isn't a problem, yeah, it's down to whatever gun can be cheaply produced in volume. (I'm sympathetic to the idea that a stamped-receiver semiauto might be a good idea as well)
My opinion here is influenced by the way lever-actions gained so much popularity in warfare and the old West even though bolt-actions were an older design.
> And a lot easier to make strong?
I imagine that's a function of metallurgy in either case. The grizzly-killing lever-action .45-70s in existence today are 140-year old designs scaled up with better materials.
Revolvers have hung onto their reputation for superior reliability with some people but there's so much that can go wrong, and so much that's pretty difficult to fix. In contrast you can build a semiauto that can be taken completely apart without any special tools or knowledge.
For a 1911 design for example, the actual patent and patent drawings would not quite be enough give you the dimensions nor location of the swinging link. It would take either quite a bit of tinkering, or sitting around and mathing (or both) to figure it out. Certainly not impossible, but I think the effort required goes a bit beyond your intention when you said 'basic level of machine shop skill'.
If you were stuck in your position, an optimist in human nature would pick something like a break-open shotgun. Not useless for self defense, but really useful for hunting - which you presumably would have to do for a bit while bootstrapping civilization again. If you weren't so optimistic... oh ya, totally an open bolt SMG.