In all honesty, mileage doesn't matter on these engines. You're talking about the 4.0, which is easily one of the most tractor like, bullet proof engines ever made. It seriously is a beast in terms of durability. When things go bad on these engines, it's typically something like an O2 sensor, a throttle sensor, a catalytic converter, or something electrical. It's rarely ever an internal engine component. It's not uncommon to see these engines with 300k mile on them still going strong.
What's going to matter the most is who owned it and how they maintained it. The more maintenance records they have, the more you know they cared for it.
You're smart to look for a mostly stock TJ. The ones that are stock and unmolested are usually the ones that were more taken care of and cared for. There's a lot of beat to piss TJs out there, and most of them are easily identifiable by all the cheap and poor modifications that people did to them.
Your biggest thing to watch out for will be rust, hands down. Get underneath the frame of any TJ you go to look at and inspect it thoroughly for rust. A little surface rust isn't an issue, but major rust is a huge issue, and you should walk away at that point, no matter how cheap they are selling it for (unless you want a huge, expensive project).
Read this thread, it has some good examples of acceptable rust, and non-acceptable rust:
What should I look for when buying a used Wrangler TJ?
I wouldn't worry about an engine rebuild or a remanufactured engine, but only if the guy who is selling it has the paperwork to back up those claims. Otherwise I would dismiss it as a seller who is lying to try to sell their vehicle. Anyone who went through the trouble of rebuilding their engine or swapping in a remanufactured engine, would surely have some paperwork to prove it, even if it's just a credit card statement.
Of those two TJs you linked to, I actually prefer the white one. It has higher miles, yes, but it also looks cleaner and more taken care of. It's also very possible that a lot of those miles are just from towing it behind an RV. While that's hard to prove, I know that lots of people do this with their TJs, and the miles can add up.
Also, do not let sellers try and convince you that their mods equal more value (or a higher asking price). Unless it's a TJ with a nice, expensive lift like a Currie, Savvy, OME, or Metalcloak, then it's not worth paying extra for. Rough Country, Skyjacker and Zone lifts are all cheap, low quality lifts.
For 10k you may have to look a bit harder to find a nice TJ, but I think you're on the right track. Hell, that white one is worth looking at if you ask me!