A and AAAA
An A record points a name at an IPv4 address, AAAA does the same for IPv6. This is what makes yourbrand.com open your server.
CNAME
An alias. www as a CNAME of the bare domain means you maintain the address in one place. A CNAME cannot sit on the bare domain itself in classic DNS, which is why the root usually gets an A record instead.
MX
Where mail for the domain should go. Independent of the site: mail can live with one provider while the site runs on another. Priority numbers decide the order, lower first.
TXT
Free form text used for verification and for mail authentication. SPF and DKIM records both live here, and getting them wrong is the usual reason mail lands in spam.
NS
Delegates the whole zone. Change these and every other record has to exist wherever the new nameservers are, which is the single most common way a site goes dark during a migration.
TTL, the one number worth planning
Resolvers cache answers for the length of the TTL. Lower it to five minutes a day before a planned move, then raise it again once the change has settled.