Wanted: Immortality on a Budget

I want to write my name in the wet concrete of the universe and get something that will say, "Joelogon was here," forever -- or as close as I can get. It'd be a monument, or at least a marker, of my existence. So here's the question:

What's the longest-lasting physical artifact that I can buy, create, or commission (at any given price point) to leave behind?

A Kilroy was here reference if you were wondering.

I explicitly say "physical artifact" to rule out flaky and intangible things like radio messages beamed out into space, true love, and the genetic legacy left to my (as yet notional) descendants.

I want something that I can hold, that can later be analyzed and puzzled over by alien archeologists in the far-distant future.

Or something I can revisit when I get nostalgic for my corporeal existence every once in an eon after I've Ascended as a pure energy being in a higher plane of existence.

10,000 years is chump change -- I'm talking at least a million years. We probably have a hard stop a few billion years from now when the Sun grows into a red giant, but I realize I'm not going to be spending a lot on this project, so even a mere billion years is probably out of scope (even though the oldest known rocks are estimated to be about 4 billion years old).

While we're setting some boundaries, let's add a few more:

• We're stuck in the gravity well: No launching of objects into interstellar space.
• Set it and forget it: No caretaker cults to polish and maintain the object.
• Readily available, existing materials: Yes, I know the singularity is right around the corner. But I'm talking about materials that exist in usable quantities now.
• Recognizably personalized: Has to be something I've marked as my own. No pointing at the Moon and saying "Mine!"

I'm thinking about a layered approach -- say, a pure platinum sphere, encased in glass...and that's where I get stuck. Don't have clue. Materials scientists, weigh in.

Where should I keep it?
Say we solve the materials science issue -- what about the geography? Where would you keep an artifact you want to last forever?

We've got an object that's supposed to outlast humanity, and anyway, we want to keep it away from people. The last thing we need is some crackhead from the dregs of a far-future civilization breaking the thing open to sell the shiny metal bits to a pawnshop.

So figure in shipping and handling costs to get the thing drop-shipped to an isolated area. Which one: Find some geographically stable desert and bury it? Get under the Antarctic ice sheet? Or take a boat ride over to the Mariana Trench and throw the thing overboard?

Until the sun explodes, what are the other major threats my artifact would face: Corrosion, erosion, tectonic activity? Countless cycles of temperature fluctuations?

Anyway, I don't have a clue, so I'd like to hear some ideas for objects at $100, $1,000, $10,000, or the price point of your choosing.