Your overall goal should be to get done with the New War quest and clear the star chart. You need to be progressing toward arbitrations and steel path and the New war is required.
Wisp and Revenant are very solid choices for early game and scale all the way into late game. Wisp's motes in combination with breach surge is super powerful. Revenant is basically unkillable if you play him correctly. As a bonus both are current primes so they are easy to farm. Hildryn and Grendel primes are very good as well and similarly easy to farm.
I also find Limbo *super* useful on an early account if you play solo. There are many mission types where you need zero interaction with enemies to complete them, spy and sabotage, etc. If you sit in the rift 100% of the time the enemies can be level 9999 and it doesn't matter. Combine with a shade sentinel for best effect. For an example I would use Limbo to solo Kuva Flood missions to farm the requiem mods needed to get into fighting Kuva Liches.
Just a couple of suggestions, many other frames work great as well.
Too many weapons are viable to really list off any. But that said, I like the Fulmin prime a lot. The Phantasm prime is powerful but not really to my liking. Many of the Lich / Sister weapons are good choices (kuva hind, kuva kohm, kuva tonkor and so on).
For end game weapon mods, it's really the same stuff that you need to get to end game. Base damage, multishot, crit chance / damage and all of the elements in 90% and 60/60%. What I would add to that list is the galvanized mods (arbitrations) and the weapon arcanes (steel path acolytes).