Hood of Shadows, +1 Assassin’s Blade, and Masterworks Thieves Tools are a great start.
Melee to-hit, saves (especially Will) and HP are the stats most in need of improvement.
Ring of Sirenbane (~$5) or Ring of Iron Will ($1) would do more good than the Ring of Reflexes.
For the open charm slot, any of Charm of Health, Charm of the Sea Snake, or Charm of the Sea Orc would help HP.
For the open Ioun Stone slots, all of the following are inexpensive: Moon Orb, Norse Opal, and Tsavorite Prism. Faceted Amber and Iridescent Spindle are also inexpensive but can be situationally useful.
Honorable mentions at slightly higher price points: IS Stalker’s Orb, Stalker’s Prism, and Beryl Prism. The Stalker items would help with saves. IS Beryl Prism is a solid add to any rare build.
For FoP, Moon Dog is a great option (although useless if there are no Incorporeal monsters). Stalker Squirrel offers one-time 6 points of damage. Cricket is also handy as a backup.