Well back when i had the young-argo-craze as a young noob hunter i found it easy like heck to just take them most of the way down with a Breer M2A(L) and then as a finisher use my lucky TT-fist when their health dropped below crit-will-be-overkill-levels
but then i could at least do it completely unarmored and just use the TT fap between kills if they got to hit me once or twice before dying
breer p4a + a104 is the most eco for lower levels when looking at weapons alone. Other viable weapon options are breer p5a or korss 400 + a104 (higher amps will also add to the eco with these two weapons.) Also, a tagging weapon such as riker ul2 is not a bad choice as it has pretty good range (you can also add an amp to that as well). Finally if we are talking strictly eco you can consider adding a finishing weapon as not to overkill on the final shots. I will leave it up to you to do the research on that one.
Now with lower dps weapons you will have more armor and fap decay because it takes longer to kill the mob. I would suggest vivo t1 inbetween mobs to heal yourself.
As for armor choices... use the armor advisor tool on www.entropiawiki.com. ex guardian + 4c is actually an ok armor setup if you want a certain amount of damage on argos. So its not always the obvious choices.
Record your results... if you are getting killed on fap and armor costs increase the DPS of your weapon or go lower maturities.
I did 200 ped argo runs with a variety of setups, and found the ul2+103 and p4a+a104 to let me kill the most argos for a given amount of ped. Was a bit slower than I wanted at times though, so p5a+a104/5/6 is still quite eco and faster.
time is money = use biggest launcher u have skill for
Seriously, id advise to get a low mu rifle - riker / lrxx and h400 or pa5 biggest amp u can get from the omegatron series. Then get a melee finisher. Fist or short blade. That way u will hunt eco fast and skill a bit melee on the side. Use rifle for tagger and pistol for main damage and fist/blade to finish.
For armor its not too important as long as its not overprot and u dont combat fap. pixie gnome rascal etc with without platings. The difference i think will be marginal on eco.
Also you can consider using a rocket launcher to finish if u have multiple mobs on u. Might not be eco, but thats also nice skills and you will also damage the next mob on killl list.