Just a [Kuva Chakkhurr] build for general use.

You can swap around Damage types as needed, say, swap for radiation while Eidolon hunting, though your Chakkhurr's innate damage type will boost or add additional types whether or not you build for it, so if specifically used for Eidolons a radiation Chakkhurr would be best.

Keep in mind that [Kuva Chakkhurr] deals improved damage on headshots.

Been using it as my main primary since my first lich and it's carried me all the way from MR5, oneshotting most enemies, almost guarenteed on headshots, and it's explosion and multishot makes it good for clearing waves of enemies at once from any range, though best performance would be at mid or long so you don't knock yourself back.

I'd also recommend a secondary with decent fire rate/reload and/or explosive as the [Kuva Chakkhurr] has a relatively small magazine and low reload speed so it pays to be able to quickly clear waves to get any enemies out of your face before reloading as any knockback or crowd control effect will interrupt the reload.