Moving a domain takes about a week: unlock at the current registrar, get the authorisation code, initiate at the new one, approve the confirmation email. Every registrar on this list handles it competently.
Four things catch people. ICANN blocks transfers within sixty days of registration or a previous transfer, so plan around it. A transfer adds a year of registration and you pay for it, you're not losing time, but you are paying up front. WHOIS privacy can mask the administrative contact address the confirmation email goes to, so check it's reachable before you start. And DNS records do not travel with the registration.
That last one is the classic outage: someone transfers a domain, the nameservers change, every record vanishes, and the site goes dark. Export your zone file first, recreate it at the destination, confirm it resolves, then flip the nameservers. Done in that order the transfer is invisible to users.
Whichever registrar you land on, enable registrar lock and two-factor authentication on day one. Domain theft happens through account compromise and social engineering, not through clever DNS attacks, and those two settings are what stands between a compromised inbox and someone else controlling your domain.