Linderhof --> Oberammergau --> Neuschwanstein - Day trip by rental car

I can't help you with travel times, but I do know that Oberammergau is totally uninspiring.
Instead go to Ettal (some 4 kilometers from Oberammergau) and let yourself be overwhelmed by the interior of the monastery. The Wieskirche, which you pass on your way to or from Oberammergau, is also a gem of a church.

You will likely need more than 2 hours at Neuschwanstein. Are you planning to go inside? Will you see Hoenschwangau Castle also while there- or the museum? Once you park near the castle, you will have a mile plus walk up to the castle (and later back down), plus whatever wait time for entry, tour time, etc. If you walk to Mary's bridge for the photo money shot that's more time yet. There are transportation options up to the castle if you don't want to walk (usually) but lengthy lines to get to them. You could easily spend a full day exploring around Neuschwanstein, but minimally, realistically, you'll probably want to allocate close to a half day.
Lisa

P.S. I vote for including the Wieskirche too- stunning!

Should we do Linderhof-->Oberammergau-->Neuschwanstein or the other way around?

I'd rather do Oberammergau (or rather Ettal as suggested by @tomfromleiden) > Linderhof > Neuschwanstein. The shortest way to go from Linderhof to Neuschwanstein ist through Austria. When leaving Linderhof turn right at the main road to Plansee / Reutte and from Reutte switch back into Bavaria to Füssen and Neuschwanstein. Google times are not realistic, at least not for Germany; I'd add 25%.

The tour in Linderhof is short (max. 30 min) but the park is worth seeing (regrettably, the grotto is closed) - I'd calculate at least two hours and one hour (driving included) for Ettal. Realistically, since you will want to have lunch too (there is a restaurant at Linderhof - which I personally dislike - and a couple of others in the Graswangtal nearby) and driving from Linderhof to Schwangau is ca. 50 min, your Neuschwanstein tour would be in the afternoon. Please note that you have to pick up your pre-booked tickets one hour before youre scheduled tour time at the latest. And then you might want to have some time to explore the beautiful surroundigs of Neuschwanstein, e.g. going up by cable car to the Tegelberg.

I've never been to Neuschwanstein, but I've seen several reports declaring the tour to be disappointing. Only 30 mins and a handful of rooms. The fame of Neuschwanstein is indeed the exterior and the setting. Skipping the tour would give you much more freedom in planning your day trip.

What time should we book our online reservations to Neuschwanstein?

First you have to decide which route you are taking. If you are going to Neuschwanstein last, you better make sure you allow plenty of time to get there allowing for spending more time at Linderhof, traffic delays, getting lost, etc. The ticket kiosk at Hohenschwangau.de says you must pick up your tickets one hour before your tour time. You'll spend at least half, perhaps more, of the time walking up the road to the castle. Then the tour takes 40 minutes and the walk down another half hour, so if all goes well 10 minutes more than 2 hours.

Other than Munich to Linderhof, the times look realistic. ViaMichelin gives the time from Munich to Linderhof at more like 1 hr 30 min.

Omerammergau might be uninspiring, but Ettal is just another over-the-top Rococo church and monastery, which are a-dime-a-dozen in Bavaria. Same with Wieskirche. I'd rather spend the time in Oberammergau. Half an hour is hardly enough time for Oberammergau; I spent two nights there with Linderhof (6+ hours) in between. An hour and a half is hardly enough time for Linderhof. By the time you go to the kiosk to get you ticket, walk to the palace, and take the ½ hour tour, there is really not enough time to tour the extensive grounds (even with the Grotto being closed). I spent an entire day there (including lunch and the Grotto).

Why do I get the feeling this is a "check-list" tour. You seem to be more focused on how many places you can say you have been to, rather than how many places you have actually "seen".

"Is driving/following German signs ... pretty straightforward?" Some signs are in international format, others are in German. You can read German, right?

Very few signs are written in words - most are pictographs which with a little study are easily understood. It is worth als understanding the rules of the road, many laws aren't signed the way you might expect. For example, a yellow town or village limits sign means 50 kph speed at that sign. Not 200 yards past ( I took my foot off the accelerator and I still got a ticket might be your refrain ) but at the sign. There may well be a speed camera just waiting to see if you do slow down. You won't see a 50 kph sign, you just have to know the law. There also won't be a kph sign (unless it is kept low for other reasons) when you leave the town, you'll have the same yellow town limits sign but with a red diagonal bar on it which says to resume the national speed limit.

And there are a few other nuances. I suggest you study up on them. Once you know, it is very easy. Don't worry, if you made a mistake, even a tiny one, some grumpy old lady in another car nearby will shout at you.

I was once on an SEV bus to the next station when we came to a T intersection with a rather long, complicated, special instruction for using that intersection. There wasn't really time to pull out your iPad and translate the sign.

Very few signs are written in words - most are pictographs which with
a little study are easily understood.

But how many Americans bother to study them at all?

Hi,

I would head first to Neuschwanstein. It's the busiest and most popular on your list. I'd also skip Oberammergau.

"Very few signs are written in words - most are pictographs which with
a little study are easily understood.
But how many Americans bother to study them at all?"

I do and a few people I know who traveled also did before their trip. Don't assume everyone is lazy.

It isn't necessary to knock places without having a clue of what the poster would be interested in.

In my case, I am a fan of architecture, particularly enjoying what I don't get to see at home. There's not a lot of Baroque or Rococo in and around London, so when I can get a big handful I am happy.

In my opinion, Ettel is well worthy of a stop, and it is very convenient. So is its restaurant.

Two things are particularly attractive about Oberammergau (plus the play every 10 years), the paintings on the buildings and wood carvers. If the religious alter and angel carvings are interesting to you there are plenty of shops with a huge variety. You won't find many places where most of the buildings are decorated with interesting paintings.

Half an hour in my opinion shortchanges these two special places.

On the other hand if neither of these two does anything for you, keep on driving past.