I own several trademarks that tie to my domains, as this allows me to register/own domains in other markets. That is for me the value of the trademark, as some countries won't let you own a domain unless you are a local company in that country or you have a international trademark for the brand/domain itself. Getting a trademark in the US costs less then $100 and can be done within a couple weeks, so really no reason not to do it. Just don't get into having to pay large amounts of money for this, as you don't need the most expensive TM company with the most costly lawyers to do it for you. Just need a credit card, about 1 hour of your time and you can register a trademark, any person or company can own a trademark in the US. You don't need to be a US person or US company.

If you are outside of the US I wouldn't buy the .net, buying your local country domain will give you much better outcome in terms of SEO and local branding. But if you are within the US, then don't buy the .net, as there is so little use of that domain extension you'd better buying a .org at least people put value in that. But if the .org won't match your brand/service/product then you can try something like the current hyped domain .io but these have their own issues, .io might even all be turned off/or have absurd pricing after the "war" over its ownership is finished. This happened with .tv everybody hyped it, nobody outside of the domain space ever understood it was a domain and now you'll almost never see a .tv domain, yet in the peak they where everywhere (like .io). I don't advice going after the 100's of other domain extensions, as while they are fun to play with from a pure ad/sending traffic into them, it is really hard to get a user to understand how to type the email addresses or even what to tell others the site is. This coming from someone who own's 1,000's of domains, and I even own a really "unique" one: https://search.engine.optimization.training/ but again this is just used for sending people into from ads.