Personally did ranged, melee and spell power boosts first, depending on classes, then prr and mrr.  Pretty much only make a difference in 1st 3ish levels, but what else are you going to spend rems on?

The mysterious cloaks come 1st IMO.  Also limited time availability.

Cloaks and Bracers are first, imo, too.  Very useful.  The FoM pot is solid for non-caster types.  After that, it gets dicey.  1 point of MP/RP is clearly more valuable than 1 point of USP, PRR or MRR, just on percentages and formula.

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Since you can trade it to Diadem of Fire ))

My take on the remnant rewards was to stockpile the the remnants until the non-standard items became available.  While the power increase tomes are okay, they're always available.  SSG only seems to add the non-standard items to the vendor every 6 months or whenever someone on the mobos remembers to remind them that it has been a while.

Especially if you're doing hTRs and rTRs go for a full set of the bracers and/or cloaks.  Get the lvl 7, 14 and 21 versions.   Those have a yellow and colorless slot.  I slotted a topaz of feather falling and a master's gift aug into each of them. 

Having all three levels of that with the same augs makes it easy to fit into a template with Cannith and Slave Lords crafted gear while you level.  Reducing the amount of time spent playing gear tetris is more time you can spend leveling.

As Rubbins pointed out, the bracers seems to fit better with caster gear.  I think the cloak is easier to slot with melee builds.

Once you have those, go for whatever Eternal potions you want next.  In my opinion, the FoM potion is probably the most universally useful, followed by the Displacement and Death Ward ones.

Once you manage to snag those, you can then get the power increasing tomes as you gather enough rems without having to wait for the few times a year SSG remembers that they have a remnant vendor.