We just purchased an 07 LR3 HSE with 93k miles on it for $18900. The key is finding a decent vehicle. Ours was a 2 owner ex-lease CA car. Super clean. Look for trucks that are obviously taken care of & well maintained.
We did notice a small leak in the steering rack & the front diff before purchase. Going in, I know I'd be changing the oil, replacing the MAF, O2 sensor, filters etcl. It already had new brake rotors/pads or I would have changed those too. Tires were also at 85%. The transmission pan has a small leak. Am planning to replace the pan (which also has the filter built in to it) and replace the fluid. The transmission fluid is also ridiculously expensive so keep that in mind. Cooling system is solid or else I would have replaced all the hoses(will do that in about another 10-15k miles). All the above is what I would have done on any used vehicle I purchased. The largest possible single expense here is possibly having to replace the steering rack. Rebuilt will run around $350-500 for the part. I'm keeping an eye on it. If it is a small leak, I may let it go for now.
The labor can be ridiculous so finding a competent non-dealer mechanic is key. Like you, I am willing and able to work on a lot of the smaller items myself & take it the mechanic for the big stuff.
Also, it is surprising how cheap the parts are compared to BMW parts. The parts themselves are not much more expensive then Honda parts. But you do have a lot more parts than a comparable Honda (such as the air springs and all the related parts). It is the accessories that will **** the bank account. I'm stunned at the prices of racks, footboards etc. But the only accessory I'm planning to purchase are OEM LR rubber mats.
The thing to remember is that for what you are paying, you get an absolutely amazing vehicle. I've driven Hondas for the last 20 years or so. My current commuter car is an 06 Accord VP 5sp with 128k miles that runs great. But I'm thoroghly enjoying the LR3. The ride, quality, interior & capabilities are amazing. The way the doors close feel incredible. Considering what you pay, I believe it is a bargain & I think the 07 hits the sweet spot. The values are there because of the bad tast the previous Discovery left in people's mind due to the unreliability. The 05 & 06 had a couple of issues with water leaking into the interior etc. which the 07 seem to have fixed. And if you look at LR4 prices, they are not depreciating nearly as much as the LR3 has. And as long as you stay on top of the maintenance, you'll be fine. Plus this is a highly engineered vehicle & to me, it is worth the expense of maintenance. My Accord, on the other hand, is a mass produced car that does not incite much emotion from me besides being a dependle vehicle that is good for the job I need it to do.
I hope this helps & good luck with which ever vehicle you end up buying.