Normally this run could be shortened to 7 missions instead of my 4 missions taken at Eaton. By jumping with the ships back and forth cycles pass till the needed missions show up that are:
Styk-Reinforcement Mission -> The 3 Talon Davion* Missions -> The 3 Tharkad Missions
* Davion Campaign has missions that take shorter time to complete.

But only a great marksman with light mechs could even complete these missions. I am not really the one that could do it though I didn't really try to run just the 7 missions! So i earned some cash from Eaton missions to get bigger mechs and then take the 7 missions needed for Davion Campaign completion. The deeper I go into the campaign the more precise the enemy mechs become. Though I haven't tried but I think that if I take the harders difficulty on the last Davion Mission it would be the same as with the easiest.

Mech Choice:

* - I used

Light mechs:
Cougar* - In my opinion is the best light mech. Good enough speed. Plenty of weapon slots and tough enough to stay alive. Puma is too slow and easily gets overheated.
Uller - Used for mercs because of lack of Cougars.
Flea - Didn't have anything else to give to mercs. I think fleas are quite useless and their speed doesn't make it up.

Medium mechs:
Hellhound* - Can have autocannons added that do enough punch against torsos and armored enough to be as bait to keep my mercs alive.
Uziel - I like Laser weapons so I like Uziel that can have PPC's as sniper weapons.

Heavy mechs:
Catapult - Used because savaged from the third eaton mission.
Black Knight - The best laser based Mech. Nova cat gets overheated too fast.

Assault mechs:
Daishi - Can have a great arsenal of weapons.
Sunder - For PPC count
Longbow - Either as a finisher of mechs or a weakener of mechs.
Awesome* - 2 PPC's are enough to get high speed and normal amount of armor
Mad Cat Mark 2* - Can have jumpjets which are quite vital for the Overlord mission by jumping up and taking a shot at the Overlord. AI controlled mercs have some trouble targeting that dropship.