Quiet around here...
Sup! I just got my LR3 not too long back as well. However, I've got a little mudding/wheeling experience.
The gear you take with you is dependent on what you're going to be doing. If you're going wheeling and trying to climb rocks, an axe isn't likely to do you much service. If you're going out to get muddy, I'd say take the following -- NOT in order of importance
Hi-Lift Jack
Good Spare Tire
Shovel
Axe
Leather Gloves
Flashlight
Buddy in 2nd Vehicle
CB (portable is fine)
Bubba Rope
D-Rings
Hitch Adapter for D-Rings
Rubberized Mats
Good Boots
A couple things to consider here...
1. If you go by yourself and get stuck, you'll need to call a tow truck. Tows from the sticks back to civilization are PRICEY. If you have a second vehicle around it can make getting help possible where it otherwise may not be. A second vehicle is also helpful if you get stuck, as they can likely pull you out.
2. Being able to communicate on the trail is critical. Having a portal hand-held CB in each car makes it that much easier to coordinate.
3. If you high center on a log because mud gives way from a tire (yes, this happened to me) it's 10x's easier to get unstuck if you can simply cut the log away. This is also where the shovel can come in.
4. Hitch adapter with D-Ring. Install this before you even get going to ensure that you don't have to futz with putting it together while stuck. For all you know, you may not be able to see the receiver to put it in/get it setup once you're stuck. I think Rugged Ridge makes this unit.
5. Bring a good set of leather gloves, because an axe and/or shovel will likely tear your hands up if used for any length of time. This is just basics to avoid injury out in the sticks.
6. Get a hi-lift jack. Despite being a jack, it can serve as a winching tool if need be down the line. Speaking of line, I didn't mention it above, but if you don't have a line to use in a winching situation, then you simply have yourself a jack now don't you? lol
7. Bubba Rope. This is good stuff to go with the D-Rings and hitch receiver if you need to be pulled out. Check out some videos on youtube and you'll see what I mean.
8. Flashlight. I'd get a triple D Cell LED Maglight. The LED is way more efficient than a bulb as you can imagine and you'll pretty much never need to worry about batteries. I think I've had mine for four years now and haven't had to change the batteries yet.

This is a good tool just in case you run into darkness or need to shine up underneath your rig -- into a wheel well maybe. This should probably be in the car at all times anyway.
9. Good spare tire for obvious reasons. Guys who go wheeling and really push the limits usually bring two spare tires. Probably not necessary if you're only wheeling in our area.
10. Rubberized Mats -- These are great, because you will get muddy. You live in the PNW and it's pretty much a given. The muddier you are, the more you'll wish you had them if you go without them.
11. Boots -- You'll want a decent pair of boots that can take the mud. Jumping out of the car in Nike's, only to be met by 6" of mud is never a good time.
These are the core basics that you'll need to go out and have a decent time. Go without them and you're gonna have a bad time <insert meme here>.
Cheers!
reethax0r