Yes. If it's a permanent move, then you need a 301 "permanent redirect"
It would be unwise and potentially dangerous to your site to use an inappropriate forwarding method.
Yes, there are downsides to using a 301, and on occasion (especially if the site is rebuilt, as well as moved), it can be very difficult. For most people, there will be a dip, then a gradual rise - not *quite* reaching the 'old' status until the quality of incoming links matches the old, as well as surviving the 'aging delay'.
But using the 'wrong' forwarding method - especially a 302 - can drop you in deeper water. Almost certainly, if you ever lost control of the 'old' domain, and quite likely even if you maintain it.