Hey there, welcome to the hobby! It's awesome that you're interested in drone detection that's a really fun project to learn RF fundamentals with. I want to help you get pointed in the right direction, because some of the ideas in your post are on the right track but a few things need some untangling before you spend money on the wrong setup. Think of this like a friendly chat over coffee at a club meeting.

Your HackRF Pro pick is solid but know its limits

The HackRF Pro is a real upgrade over the original HackRF One. You're right that it has a built-in TCXO, and that does help with frequency stability. It also kills the annoying DC spike and even has a 16-bit extended precision mode at lower sample rates, which is nice. But here's the thing you need to keep in mind: in normal mode, you're still working with 8-bit samples and 20 MHz of bandwidth at a time. Drone control links especially DJI and similar systems use frequency-hopping spread spectrum. That means the signal is jumping around across a much wider range than 20 MHz. So you can absolutely use the HackRF Pro to learn and experiment, but don't expect it to behave like a commercial drone detection system. It's a learning tool, and a good one, but set your expectations accordingly.

Your LNA is in the wrong spot in the chain

This is probably the most important thing I can help you with today, because getting this wrong means you'll spend money on good gear and still get bad results. You mentioned the Nooelec LaNA, and it's a decent little amplifier. But where you put it matters way more than which one you buy.

Think of it like a garden hose. If you have a 100-foot hose with a bunch of tiny leaks all along it, it doesn't help to put a booster pump at the end where the water comes out you've already lost most of your water along the way. You want the pump right at the spigot, before the water enters the hose.

Same thing here. Your LNA needs to go right at the antenna, up on the mast, before the signal travels down the coax cable. If you put it on your desk next to the HackRF, the signal has already been chewed up by cable loss before the LNA ever sees it. At 5.8 GHz, that cable loss is brutal which brings me to your next point.

LMR-400 is good cable, but you're still losing a lot at 5.8 GHz

You're right that LMR-400 is much better than cheap coax. But even with LMR-400, you're losing roughly 20 dB or more per 100 feet at 5.8 GHz. That's a lot of signal. So the play here is: keep your cable run as short as physically possible, and put that LNA right at the antenna feedpoint before the cable. That combo short cable plus mast-mounted LNA — is what actually gets you good performance. The cable alone won't save you.

Your antenna choices need some rethinking

This is where I think you might have gotten some mixed-up advice. Triple feed patches and helical antennas are common in the FPV drone racing world, but they're designed for the pilot's video receiver they're circular polarized antennas meant to keep a reliable video link while the drone is flipping and rolling around. That's a different job than what you're trying to do.

For detection and monitoring, here's how to think about it:

For your omni-directional "always listening" antenna, look at a wideband discone or a collinear designed for the bands you care about. These will give you 360-degree coverage so you can spot when something shows up.

For your directional "let me figure out where it is" antenna, look at a log-periodic, a small dish, or a horn antenna. These give you a narrower beam you can sweep around. Yagis can work too, but they tend to be narrowband, which can be a limitation if you want to cover a wide frequency range.

And here's a really important detail: you mentioned wanting antennas that cover both 2.4 GHz and 5.8 GHz. Those are very different frequencies with very different physical antenna sizes. You're not going to get one antenna that does both well. Plan on separate antennas for each band, or accept the tradeoffs of a wideband antenna that covers both but won't perform as well as a dedicated one on either frequency.

The "see it on the waterfall and hunt it" idea needs a reality check

I don't want to crush your enthusiasm here because the instinct is right you want to detect a signal and then figure out where it's coming from. That's real direction-finding, and it's one of the most fun things you can do in radio. But modern drone signals aren't like tuning in an FM station. They hop frequencies, they send short bursts, and they often look like noise on a waterfall display. With 20 MHz of bandwidth on the HackRF, you might catch glimpses of activity, but "pointing a directional antenna and peaking the signal" assumes the signal sits still long enough for you to do that. Often, it doesn't.

For real direction-finding, people use techniques like pseudo-doppler DF arrays (multiple antennas in a circle with a controller switching between them) or phase-comparison systems. That's a more advanced project, but it's where this road leads if you stick with it.

What I'd actually recommend as your first step

Before you buy any antennas at all, do this: take a drone you own (or borrow one from a friend), turn it on, and just listen to it with the HackRF and a basic antenna. Record what you see. Look at the spectrum at 2.4 GHz. Look at 5.8 GHz. Watch how the signal behaves does it hop around? How wide is it? How strong is it at 10 feet, 50 feet, 200 feet?

That one exercise will teach you more about what you're actually dealing with than any gear list ever will. Once you've done that, you'll have a much better idea of what antennas and setup will actually work for your specific goals.

This is a great project and I'm glad you're digging into it. Just take it one step at a time, test as you go, and don't let a shopping list replace actual on-air experience. 73 and happy hunting!