Just scanned my local CL and really nothing. Hopefully your area has better asking prices on used machines. Nothing there - any size - under $10k that would meet your needs except a 1980s off brand which would carry a lot of risk of ever fixing what breaks...
$6-$7k is going to be a very limiting factor, unless your used market is pretty soft. I think that will be the expectation that needs reset. Most of the smaller machines you won't even find a 2WD variant. The subcompacts need 4wd because the rears are going to break traction - add a bucketful of something out front and the rears are real likely to break traction. Just the corner of a bush hog catching a high dirt spot would have me spinning rears at times on the 25HP machine I had & it wasn't the smallest. So unless you're wanting a larger older tractor, probably retrofitted with an aftermarket loader, crossing 2WD off the list doesn't really do much for you.
The little subcompacts are neat. They can do a lot. But reality there is just some stuff you're not gonna get done (in a reasonable amount of time, or physically incapable). Kubota BX 2380, JD 1025, MF GC1715, LS MT1, etc - everyone makes one. So they are "real tractors" - not just a glorified lawn mower. But you still have to have reasonable expectations of what the limitations are and realize they will work above their limitations, but will break doing so. But even at that, at least around here, you're looking at $9kish for a decent used one. Any less is a scam or something really broken.
From there, prices just go up, unless age, condition, bazillion hours, etc warrants a smaller price.
So.....what options that leave you? If that $6-7k is stuffed under your mattress, hit up the auctions, especially estate auctions. Otherwise, spread the word if you're in no rush. Friends, family, co-workers, church members - someone you know knows someone that has a tractor they'd consider selling. Might find an older machine in good shape and with a loader that way. I woudn't want a tractor without a loader. Primary reason I even have it is to be a dirt-mover. However, the tasks you listed can all be done w/o a loader. Boom pole & carry-all can do some of what a loader can, maybe just not as convenient. Heck, think of how much you could really do with an 8N in good shape and large assortment of implements....
From the limited info we have on your needs & situation....to me I'd think something similar to a Kubota
L3301 would be about the smallest you'd want. Maybe get by with smaller, but around there is where it's really starting to meet your needs in capability. So that means you're looking for something along the lines of an older Kubota
L2650 or thereabout....