Generally I would advice you to focus your with to buy stuff on the mods offered by the syndicates. e.g. the Rhino mods from Steel Meridian. The mods/auguments are clearly much more important than weapons.
The point is, Augment mods cost 25k standing while weapons cost 125k. Therefore I think it is more efficient to redeem a weapon as a rank-up reward (assuming it's possible in the first place). I do agree that Augments are necessary and I'll be buying them for Standing ASAP.
You rep grind sounds perfect btw. Steel Meridian Sigil + Suda missions + Steel missions = progress in 4 factions
Best to indeed use Suda for this, as her Sigil is just -50% Red Veil rep (as opposed to Arbiters' -100%). Even at worst case scenario this allows to lessen the negative impact to Red Veil standing.
Also what Syndicate missions are also useful for is bypassing the star map nodes. For example, there's one Rescue node on Sedna that kept half of it locked away. I put that one on backburner, then found out that there was a Syndicate Disruption mission instead. I hate Rescue missions (mainly because they are bugged... the hostage can get teleported elsewhere or get stuck), so here's that.
(I also hated Disruption missions until I found out that Rhino Stomp can stun Demolition units.)
The Invasion missions can also change the mission type, but they have increased enemy level (while Syndicate missions have a fixed level and it might be lower or higher than normal for that node).