You're getting my suggestion back to front. Don't grind to get into Eden, make use of Eden (and other side content) when you have the ilevel to get into it but not higher MSQ content.
Doing content earns you tomes. Tomes give you free gear. You'll get an assortment of gear as you work through the MSQ dungeons along with tomes to buy more.
Even if you plan to do nothing but MSQ, it doesn't make sense to go out and buy a full set of i510 gear to tackle content that only requires i430 initially (for the 5.1 dungeon) and never needs more than i490.
If you're going to buy gear, get a weapon and enough pieces to see you over the necessary threshold* but don't pay to overgear yourself at this point.
*I would suggest aiming for i465 initially as that gets you into the 5.3 trial and Shadowbringers' final epilogue, then play through to that point, then fill any gaps in your equipment first with tome gear then either purchased gear or Eden Part 3.
Edit to add: ...and then get the rest of the Cryptlurker gear with poetics once Endwalker hits.
