I'm not the best to answer, but like Night Slasher I really learned how to play using the Vanilla Human Adept w/ Tempest ... that was my go to kit for a long time as I learned the game.
You've got some decent stuff unlocked; in addition to the GPR/TSol that Night Slasher mentioned, your Phaeston is at level V and works pretty well on the TSol. I see that you don't have many weapons mods unlocked yet, but you can put the Assault Rifle Stability mod V and Assault Rifle Mag Mod V on the Phaeston - pair it with any level of Armor Piercing ammo and the TSol can do some serious damage on Silver with his maxed passives.
If you want to use a shotgun w/ the Havoc, Katana X is perfectly fine for silver - especially if you will be Havoc Striking a lot. You can stick the Blade Attachment V on it and follow your Havoc Strike w/ a heavy melee and it will do a lot of damage. Same thing for your Scimtar, though it's only at level III - it's not a bad close range weapon though. Your Eviscerator is at VII, and is a great Silver weapon - lightweight, decent damage and range.
If you're really having trouble staying on your feet, you can try a Havoc build sans Havoc Strike. Max fitness and stim packs for extra 'tankiness' and pop a stim pack at the first sign of trouble while playing the Havoc soldier at range. You've got both 'Warfighter Package' and 'Shock Trooper Package' at level I, which will give you an additional stim pack along with some moderate assault rifle or shotgun damage.
I hope some of this helpful - there are some really good/smart folks here so be sure to search for their advice
. Have fun!