Tubeless ready?

For inner tube go with Michelin Air Stop - very high quality and most importantly they don't have removable valve cores. Some mini pumps (particularly those from Lezyne) which screw on to the valve have a tendency to remove the valve when unscrewed. Which, on a wet November Tuesday night in the middle of nowhere, is not ideal. I speak from experience.

I don't think anyone knows what "tubeless ready" actually means except that the wheel can be run tubeless if you want to (although there are people who run "ghetto tubeless" which involves putting enough tubeless rim tape on a standard rim and hoping that the tyre doesn't fall off).

If I were you, I'd start off with using an inner tube as that's what you're used to. Once you've got a few miles on it, you can then decide whether you want to try out tubeless or not. Generally, tubeless is more faff to install and more expensive, but it promises far fewer punctures and possibly better rolling resistance.

If you want to jump straight into tubeless to see what it's like, then you'll need some tubeless rim tape (or not if it's already installed on your rims), tubeless valves (may be supplied with the wheels) and some tubeless sealant. If the rim tape is applied properly, then you can usually get a tubeless tyre "seated" with just an ordinary pump (track pump preferably), but if there's small air leaks or the tyre beads aren't well lubricated (dilute washing-up liquid is your friend) then the solution is an air-tank pump or your local bike shop. An air-tank allows you to put a large volume of air into the tyre quick enough to push the beads into place before the air escapes through any leaks. Once the tyre is seated, the sealant should then resolve any small leaks.

Basically saying the same as Kil0ran, but changing the emphasis a little: looking at the spec of the bike on the Trek website, it looks likely your bike will have been supplied with tubeless ready rims, but fitted with clincher (not tubeless) tyres (Bontrager R1 Hard Case Lite) and inner tubes. So, in terms of puncture related accessories, unless you specifically want to change to tubeless, you'll just need to carry the same sort of puncture repair kit you would have 10 years ago (levers, spare tube, pump etc). 

Most bikes/wheels sold nowadays are "tubeless ready" but in my experience it doesn't mean much at all. It means it should be possible to run tubeless but a) that was possible even with non "tubeless ready" wheels back in the day and b) it can still be a faff to get set up.

It's very rare for a bike to be shipped tubeless. So you probably currently have tubes. I would say it's 50/50 whether they have shipped the bike with tubeless rim tape or standard rim tape.

The answer to your next questions depends on whether or not you want to convert to tubeless. I would say for riding on tarmac with tyres <30mm it's not worth it; stick to tubes.

Normally on my road bike I carry a spare tube (nothing fancy, I go for a cheap but brand name butyl tube - continental, schwalbe, vittoria etc) and in the first instance I fix a puncture by just swapping out the tube (making sure to identify and remove whatever cause the puncture!) I also carry a tiny tube repair kit (Park Tools Super Patch) so if the sh*t really hits the fan and I get more punctures I can at least attempt a repair.

If you want to convert to tubeless, there are various guides on the internet. This road.cc guide is decent but google will bring up hundreds more similar videos for a range of opinions: https://road.cc/content/feature/fitting-tubeless-tyres-learn-how-simple-...

If you do go down the tubeless route, then the idea is that the sealant fluid just seals any punctures - ideally before you even notice them! Sometimes you might notice a drop in pressure, and sometimes you might need to stop and encourage the sealant by positioning the hole at the bottom of the wheel. If you get a puncture that is too big for the sealant to cope with, then the next best option is to plug it with a tubeless plug. Essentially the plug is meant to largely block the hole, and then the sealant does its job to make it air tight. There are a huge number of plugs available on the market, from dirt cheap (https://road.cc/content/review/183575-genuine-innovations-tubeless-tire-...) to pretty pricey (https://road.cc/content/review/265660-dynaplug-racer-tubeless-repair-kit). If the plug doesn't work, then your final solution is to put a tube in the tyre (so you should carry a spare tube anyway!)

In terms of other accessories to carry, I do carry a chain link (and chain breaker, if not part of your multi tool). I also carry around a spare presta valve core (I have managed to snap/bend them before with clumsy pumping). I carry around a tyre boot (although you can fudge one from any suitable material - the new plastic bank notes are ideal). 

as you list a track pump, then worth having a torque wrench.

a chain tool and split link is also worthwhile, your multi tool may or may not have the chain tool.

No tubes, but you need to carry one just in case, as not all punctures will seal/self-heal - particularly at high pressures

Tubeless repair kit, which is about the same size as a traditional puncture repair kit and consists of a knife, reamer, and applicator. Topeak have one built into the PT30 mini tool (review on this site). Then you need tubeless plugs. You use the tool to prep the hole for the plug. The idea is that most punctures will self heal - thorns etc nearly always will - anything up to a 3mm cut as a rule of thumb

You install a tubeless-ready/tubeless compatible tyre and valves, add sealant (liquid latex basically) and hopefully ride for miles without a visit from the puncture fairy.

"Tubeless Ready" is a whole other can of worms. The problem is that there's no industry standard for what that means. Basically though it comes down to having a rim and tyre bead that snap together under pressure, like a car tyre. With sealant added to the tyre this forms an airtight seal. 

Having had a quick look at the current bike spec I think you'll also need to convert the wheels to tubeless. That involves replacing the rim strip with wider air tight tubeless tape and fitting tubeless valves. Trek/Bontrager have a kit for this but there are many aftermarket kits. Easy DIY job.

Depending on the tyre you might also need a tubeless tank to get the tyre to seat on the rim for the first time. You might also need new tyres - definitely if you're still running the stock tyres (R1 hard case lite?) which came with the bike.

All in, budget £100 to convert the wheels to tubeless if you need to buy a tubeless tank. Double that if you need to replace your tyres.

Is it worth it? Well, you can run lower pressures, and lower pressures reduce rolling resistance and make you faster. You no longer run the risk of snakebite punctures. Its great for hedge-cutting season because small thorn punctures will automatically seal. Bigger cuts can be more problematic, particularly at road pressures (tubeless sealant works better in high volume low pressure tyres). To keep everything running smoothly you need to change your sealant every 3-6 months which can be a messy job (but have a look at Milkit valves as they minimise mess). And there's no guarantee you won't get a puncture. I run tubeless on my MTB and tubes on my road bikes. Reason? MTB tubes are massive and carrying a spare uses too much space. There are neat solutions that allow you to stash your repair tools in bar plugs (also available for road). I can also run ridiculously low pressures which helps with comfort and grip offroad. I didn't do the same on the road because I'm a heavy rider and so even tubeless I needed to run high pressures, and very high pressures don't always work well with tubeless sealant.