Coming from almost 25 years of experience in technology, focused on web technologies, e-commerce, and business systems, I always recommend trying your hardest to get a .com domain instead of any of the other top-level-domains, unless the US is not in your target market. Everyone remembers and almost instinctively puts in .com, regardless. Even the browsers want you to use a .com. Try typing just the word "google" in the address bar and press CTRL + Enter (I think is command + enter on Mac, mine isn't near me at the moment).
For those looking for domain names, services like https://www.domainnamesoup.com/ can be helpful. They allow you to mass lookup availability and help to create new combinations for inspiration. What we ended up doing, when renaming our business (a project still in process, so not using the name publicly yet) was to create a list of words we felt gave the emotional responses we wanted. For example, you might want to give the feeling of dependability, or solid foundation, etc. so you might start using words that feel like that: stone, core, clock, etc., but maybe you want to combine that with fresh and new, so perhaps "slate" for the stone and 'clean slate' term.
Once we had our list of words, we gave them all scores on length, ease of pronouncing (not everyone speaks your native tongue, help them out with simple words), and how many of our values they hit. Then we used Excel to create a two-word mashup for each word combination. With that list, I was able to copy and paste all of them as a "<word-one><word-two>.com" value into the Domain Name Soup site, and find out which ones were available. With the unavailable domains filtered out, we then each gave a yes/no to each combo, and merged that with the scoring. So the shortest, easiest to pronounce, easiest to spell, most liked, and most on company values combination bubbled up to the top.
Prior to that, it felt like throwing darts at one balloon in a pitch-black room, and we never got anywhere.
As for registrars and who owns the domain, it is true that GoDaddy will hold on to the domain for a while, even after you've let it go, but it's to try and protect against accidental expiration and domain vultures. It used to be very common for a domain to expires, and a person would swoop in to buy it up in hopes that the original owner would be at their mercy and pay handsomely for its return. They're even worse than the squatters. While I, personally, do not care for GoDaddy anymore, they're safe to register domains through. They do, however, tend to raise the annual renewal more frequently than I care for. When I migrated my domains away from GoDaddy, it was automated and completed in minutes, with no resistance or issues. ICANN does a pretty good job of keeping the chaos to a low roar.
Hopefully, someone finds all that helpful!