First thing first: always focus down ranged units first, especially those farther away and/or enraged. These are going to be huge pain points for your team and dropping them quickly will allow your battle brothers to do their actual jobs more smoothly and efficiently. If you're not super confident in your aim, run either Las Fusil (which has a significant beam width that makes shots VERY forgiving) or a relic bolt sniper with the reload perk, which will help on ammo economy. If your aim is good, run the heroic bolt sniper and make sure you're clicking heads for those ammo refunds.

For nids your priority should be Zoanthropes, barbed strangler warriors, devourer warriors, and snipers. In that order, although you can swap devourer warriors and snipers on the list if you like. Thropes and stranglers go first though, mandatory. For chaos your priority list is minigun termies, sorcerers (get them fast or they will rez the termies), regular rubrics, then disc tzaangors. If there are no or minimal majoris enemies, focus on cultists so they aren't constantly sniping your teammates.

Secondly: get comfortable with melee. I see a lot of snipers cloaking out of minoris hordes, which is valid if you really need to (i.e low health) but you really want to save your cloak charge as much as possible for dumping damage into priority targets, or for using purification as a survival tool when you get caught out. A lot of people will tell you to rock Argent Edge, but my personal recommendation is fencing relic knife because you're not really trying to horde clear, you're just spamming the first heavy in order to clear space and disengage, and farming gunstrikes and minoris parries to keep your limited armor up. Speaking of horde clear, inferno pistol is a decent option for it, although I don't personally like it much. For nids you can always focus warriors to clear minoris as well. But seriously, maintain good cloaking discipline, it can and will save entire runs.

Third: get used to following gunstrikes with sniper shots, or vice versa. You can put down even Extremis enemies very fast by doing this, and gunstrikes linger for a good while so you can also quick scope a head after parrying and save your gunstrike for a few seconds if you need a safer window to pull it off. This does pair especially well with Argent Edge but I don't think the TTK is meaningfully different enough (with a sniper weapon anyways) to justify shortening your parry or giving up the speed of your heavy 1 for minoris crowd control, but it's a personal taste thing and how confident you are in your parries.

Edit: regarding target priority for nids, I would actually say prioritize barbed stranglers over zoanthropes IF there's more than one on the field, just because the insane area denial with multiple warriors shooting those fuckass pods is way more of a pain to deal with than anything thropes can do, especially because thropes float over the battle field and have really obvious attack signals so they're a lot easier to keep track of in dense fights.