The easiest shooter mission you can get is "exterminate scanvengers" at a threat 2 settlement. I would recommend that you spend the time to upgrade a maverick suit, tormentor and executioner to G5 first, but it is not necessary. If you spend time looking in stations you can find a g3 version of each.
In "exterminate scavengers" missions the threat level actually matters. T2 has the easiest scavengers, T3 they are harder and T4 the hardest. T2 is low security settlements, T3 is medium security settlements and T4 is high security settlements. If you do power restore missions and you get scavengers the security level of the settlement will affect the difficulty level of the scavengers that spawn.
Easiest way to find "exterminate scavengers" missions it to go to systems in bust, civil unrest, infrastructure failure, pirate attack or terrorist attack and go to settlements controlled by the faction that is in bust, civil unrest, infrastructure failure, pirate attack or terrorist attack and check a terminal in the settlement under "combat missions".
If you mod your weapons with noise suppression and audio masking, with practice you can take out 50%+ of the present scavengers before the rest even know you are there.
Use the search function at inara.cz to find the type of system you are looking for. Below are links to the site plus an example. In the example click on the "new search" button and you can see how I filled it out.
inara.cz search link
civil unrest settlements near Sol
Set the "near star system" setting to where you are. If you sign into inara.cz and have your commander linked then it will automatically pick up where you are.
Last thing, since the Power Play update, power play commandos have been dropping at abandoned settlements. If they spawn as part of the scavengers that spawn it is impossible to complete the mission since the game counts them as part of the scavengers that spawned, but the game does not count them as scavengers killed. Also it you kill them you become wanted, get a bounty on you and get notoriety. In the inara.cz search you can set the "power" setting to none. The way the system you go to is not controlled by any power and the commandos will not spawn.