Let's start from the beginning. It's a very good place to start.
Rule #1: Don't go overboard. It's a trail bike, not a lift access battle tank. I wouldn't put anything with more than 150mm on the bike, first off. People often get dreams of turning every bike they own into a dh bike, but it just isn't safe. You increase the leverage on the head tube with a longer fork, and you run the risk of breaking important bits on the bike as well as your body.
Next, your fork appears to be a 1_1/8" diameter straight steering tube. Your frame's head tube looks like a straight 1_1/2" on both top and bottom. This means you will either have to 1) get a new fork that has a straight 1_1/8" steer tube, or 2) get a tapered steer tube and a new headset that will accommodate the tapered steer tube. Either way will be fine, but I personally like the tapered tubes.
Any of the larger fork brands will be good. I personally really like the feel of Fox forks, with Rockshox a close second. Manitou is also good. X Fusion makes some awesome stuff too, and I'd put them right with Rockshox in second.
Next up: Axle type. It looks from the pictures like you have a standard quick release axle. To avoid having to get a new hub, spokes, etc, you probably will want to stay with the quick release axle. That means don't order a fork that has a 20mm thru axle or a 15mm QR axle. They won't fit. Unless you want to get the added benefits of the thru axle and are willing to get a new hub/wheel.
Next is stanchion diameter. Stanchions are the slidey parts of the fork that you don't want to scratch up. Fox, for example, sells 4 stanchion diameters. 32mm, 34mm, 36mm, and 40mm. I believe that they only sell the standard quick release on the 32mm diameter. That'd be a fine fork for you. Many people get worried about how big their stanchions are. Don't get hung up on that. They are all plenty rigid for you, unless you plan on starting to do big drops/jumps. Then you're looking more at the 36mm stanchions.
Lastly is all the adjustment you can add to the fork. You for sure want Rebound damping adjustment, and if you can afford one with compression adjustment, then that's even better. I personally do not know a single person who uses a lockout on their fork. It's more important on a rear shock, not the fork.
Then there is air vs coil/oil. Coil is simpler, but heavier. Air is lighter but you need to get a good one for it to be worth the cost.
My vote is for a Fox Float 140 or 150 in the 32mm stanchion. I rode one for 3 years and it held up incredibly well. VERY good fork.