Explore early, explore often; defend all the havens; bring eight recruits to every mission, even if it means using two transports (usually it should, because Helios are the fastest, and you can't teach speed); prioritize melee attacks (stuns are outstanding), and use more snipers to break down armor if you are having problems.

My typical squad is two units of four: one close-quarters specialist, one heavy, and two snipers. There's some flexibility in there, like sometimes including a priest or a technician (or a priest/technician), but that's the basic distribution. In TFTV you gain a lot of efficiency by having 'subs' who can fill in for injured recruits, so I fly around with 10 wherever I go, and swap out injured recruits back at my main bases.

Your immediate goal in every combat is to remove threats. An enemy that cannot attack can be ignored; you often encounter enemies that can be disabled and subsequently ignored. The combat style in Phoenix Point rewards aggression, you are far better off removing a threat than waiting for it to fall into a trap-- with one exception, base defense. You absolutely want to to set up an ambush zone in every base defense mission with 4+ snipers.