Do I need a backhoe or an excavator?

I have 3ish acres of bumpy forest on whidbey island. Much of the forest is alders that, according to a forester I hired, are about to start dying of old age. I have a neighbor with a sawmill that they're willing to sell me, and I'd like a machine to move trunks onto the sawmill, move the storm felled trunks to hugelcultur beds, dig out the roots/stumps and put those into hugelcultur beds, reshape some of the other land, build about 100' of road/driveway, and trench along about 500' of road for power conduit. I'd also like to level some ground for some small buildings.
It seems like I can buy a Case 580CK for 4-8 thousand dollars at any given time around here, but right now someone is selling a Komatsu PC05 mini excavator on tracks for 7 thousand. I'd like to spend less than 10 thousand, and I'll probably sell/list whatever I get for rent after I'm done shaping the land.

I don't want to rent something because I live about a 90 minute drive from the property that I'm working on and have no idea how many weekends it'll take to do everything I want to do.

What would you buy?

If I wanted to move logs, I would use a forklift, a skid steer, or a tractor.

The tractor is what I have experience with.

We tie a rope to the logs through a loop in the rope tied to the tractor.

I'm no expert, but the excavator would probably be easier to rent down the road.

The little excavator thingy has a thumb to (I assume) pick up logs with-
If I tie a log to a tractor, how does it get to the bed of the saw mill?

I vote for the mini X
Pros)
With tracks, you will get stuck less.
It's a mini, so it will fit in tiny spots.
360-degree spin is invaluable.
Easy to load on a trailer.

Cons)
Lightweight, many things will tip up your hoe. (You learn how to work around that.)
Smaller bucket and has less reach than a 580 extend-ahoe
You might need to call in a more appropriate machine for some jobs.

Some factors to consider.  How big are the logs and what length?  The following are my only my opinion based on experience owning a JCB 3cx and a Kubota 0457.  I bought a backhoe first because it's basically the swiss army knife of equipment.  It can do everything.   If you plan on moving loads of earth and rocks around without some kind of dump truck/trailer or many wheelbarrow loads, another win for the backhoe.  That backhoe is big enough to dig the roots and push trees over.

That mini excavator may be prone to tipping or you will have to be very careful when skidding bigger logs, slow and steady, especially on bumpy ground.  It maybe be quicker at the cleanup/landscaping.  You could level ground as you go.  Obviously, it will outmaneuver and fit in tighter spaces

Excavator probably has more selling potential down the road but in my area either of those would hold their value at those prices but don't forget that unexpected maintenance costs are a sure bet with any heavy equipment.

A backhoe with forks on the bucket will do all  of what you want.  Not the best machine for anything, but a Jack-of-all. You can buy add on forks on Amazon if you can’t find them local.

A small mini ex is not good for moving logs, it will handle posts just fine but by the time you get something big enough to cut usable lumber, it is REALLY easy to tip it if you grab off center or over extend.  

Neither machine will dig big stumps.  The ex is better for hugel building just because of maneuverability. The backhoe is better at roads because of size and the bucket.

I'm also recommending a backhoe:

-you can move the logs with the loader and chains or with a forklift attachment
-you can dig the roots of the trees
-you can grade (not as efficiently as a bulldozer though)
-you can transport material in the loader
-last and very important - you can unload pallets from a truck/container/flatbed and move them around

When building there is A LOT of material movements. I use my tractor for moving things more often than for agricultural purposes.

Well, Shahar;
You obviously need both!

bumpy forest? some backhoes can be very top heavy and trying to get them in position in hilly places can be difficult or possibly dangerous. . any idea how much your logs will weigh? might want to be sure of lifting capacity of whatever machine you invest in. I use a utility tractor to drag logs across my hilly property. utility tractors generally have lower center of gravity. it works for me but there are some logs I cant get to without hundred foot or more of cable or chain. but my property could be considered mountainous.
all the loggers around here have to use a dozer usually no bigger than a d4 or d5 to pull logs out of forest or to a staging area where it is safe to operate a skidder.
something you might consider is when your ready lease a machine for a month to get all your log moving and digging work done.
a safe all around bet might be something the size of a cat 308 with a thumb and adjustable blade

CASE 580 is considerably older than the Komatsu you are considering. Parts are certainly still available and they are pretty straightforward to work on.
An excavator that small is the second or third piece a small landowner should buy if at all. The backhoe is far, far more versatile. You could choke and skid trees that excavator could do nothing with.
Weld a hook to the bucket for a flip chain
Then get a tracked backhoe with a Drott 4way bucket

A $7,000 excavator is no deal.  If that thing starts breaking down, and it will, it's going to get exponentially more expensive to fix.  Shop rates can be $200+/hr and you have to have the equipment to haul it there, or pay $300 every ten miles for the field truck to come visit you.  

Pumps wear out, engines wear out, hoses get brittle and blow, seals wear out, pins and bushings wear out, etc.  

Revamping a homestead is a campaign, but that doesn't mean you can't rent your way to it and come out way ahead of owning old equipment.  Check for rentals and use some savvy vacation time to rent one for a week at a time.  Write down what you really want to do, and then assign times to each chore.  40 rental hours on a properly sized and newer machine will run circles around a small old machine on weekends.  You'll probably get a year's worth of projects done in 40 hours.  

Backhoe loaders are good when you need a tractor that can periodically dig and also lift light loads, can also get around faster than an excavator.    

An excavator is for when all you need to do it dig and move heavy things.  Machines have the ability to destroy themselves, and tractors with loaders are champions at that.  They will lift more than the front ends, arms, tires, and hydraulics are meant to, and they'll be junk far faster than they otherwise should.  And that amplifies the real cost of that machine.  

I just found this and have no idea if it’s accurate but it looks like it was coded in 1997 so it’s probably not hallucinating: https://www.woodweb.com/cgi-bin/calculators/calc.pl
Assuming I cut the logs to 20’ lengths (which I can’t imagine why I would need 20’ boards, maybe if I build a cabin?) and assuming they’re the same thickness at the top as at breast height, which is impossible but I have no way of estimating the taper, I’m looking at 2500 lb logs.

I love the welded hooks suggestion for getting them up on the mill bed, thanks!