TLDR: Sounds like you would want to go for Gunnery->Tactics->Guts->Piloting then.
Gunnery - all ranks: +2.5% base ranged weapon hit chance per point
Tactics would allow you to reduce penalties from LRM indirect fire, like arcing missiles over a building. Also reduces minimum ranges (for PPC), mastery of called shots, and better initiative.
Guts would Make your recoil suck less, give you extra pilot health, reduce chance of pilot death (Death Chance (140% - 5% * Guts) ), can be guarded while just standing there dishing out fire, and your heat level takes more to overheat.
Piloting makes you harder to hit and do more damage with melee, sprint further and also move after shooting if you have not moved yet
Some one else posted earlier:
There are four skills you level up from rank 1-10. At rank 5 and rank 8 you receive a special ability, but you only have two rank 5 slots and one rank 8 slot so choose wisely. These Abilities will appear on the Action Bar in the 5, 6, and 7 slots.
Gunnery - all ranks: +2.5% base ranged weapon hit chance per point
- Rank 5: Multi-Target - Action: Fire weapons at up to three targets.
- Rank 8: Breaching Shot - Passive: Attacks with a single weapon ignore Cover and Guarded on the target.
Piloting - all ranks: +2.5% base melee hit chance per point
- Rank 4: +1 Unsteady Threshold
- Rank 5: Evasive Movement - Passive: The unit generates an extra Evasive charge from movement actions.
- Rank 6: +1 max Evasion
- Rank 7: +20% sprint distance
- Rank 8: Ace Pilot - Passive: This unit can move after shooting if it has not moved yet.
- Rank 9: +1 Unsteady Threshold (+2 total)
- Rank 10: +1 max Evasion (+2 total)
Guts - all ranks: +5% bonus on survival rolls. Incapacitated Death Chance (90% - 5%*Guts), Lethal Death Chance (140% - 5% * Guts).
- Rank 4: +1 Health
- Rank 5: -1 Recoil Penalty, Bulwark - Passive: Gain Guarded when remaining stationary. (you can still shoot)
- Rank 6: +15 Overheat Threshold (redesigned, used to be 5 for every guts skill point)
- Rank 7: +1 more Health (+2 total)
- Rank 8: -1 Recoil Penalty, for a total of -2, Juggernaut - Passive: Successful Melee attacks knock your target back one Initiative Phase
- Rank 9: +15 Overheat Threshold, for a total of +30
- Rank 10: +1 more Health (+3 total)
Tactics
- Rank 4: -1 Indirect Fire Penalty
- Rank 5: -45 Minimum Range, Sensor Lock - Action: Select a target within sensor range to reveal it until the end of the current round and remove two evasive charges. Consumes your firing action.
- Rank 6: "Called Shot Bonus"
- Rank 7: -1 more Indirect Fire Penalty (-2 total)
- Rank 8: -45 Minimum Range, (-90 total), Master Tactician - Passive: Mechs piloted by this MechWarrior gain +1 Initiative, and remove one bar of Stability Damage when Reserving
- Rank 9: "Called Shot Mastery"
- Rank 10: Eliminates Indirect Fire Penalty