Custom Card Alteration Compass!
So you're considering casting aside the hum-drum of the commonality of collecting simply mint cards, and careening face-first into the pandemonious whimsy that is collecting card alterations. Excellent choice, if I may say so.
Behold, the map and never-points-north compass of navigating this M. C. Escheresque weirdscape.
When requesting a card alteration, it is perfectly fine to simply say "do what you do, man," and watch the dark arts unfold before you. But this is a path for the intrepid, for these futures are uncertain. What follows "artist's choice" is often a colorful flurry of chaos. In the end, madness may take your mind as well as your card.
It is also perfectly fine to have what you'd like dialed in precisely, with reference and charts and sticky-notes and a heart full of hope. I'll do my best to manifest the imagery in your brainmeat into reality on your card.
For everything in-between, let's take a brisk stroll through a curious garden of ideas and options that you may like to consider.
Platinum or Diamondillium?
The first decision to make is also one of the easiest. How much alteration do you want on your alteration? Platinum, (or "Single") alterations are one big change. Turning Chandra into an olde-timey pirate, or adding a giant, mildly irritated squid in the background. Diamondillium (or "Double") alterations discard caution (and much of the original art,) changing characters, backgrounds, adding or subtracting things. Leaving very little limitation for venturing into incharted, sometimes bizarre territory. If you want your Child of Alara to become Emrakul feasting on zombie hot-dogs, Diamondillium is probably the choice for you.
Playable or Unfettered?
Your next question is about where your alter will make its home. Will it be out there, showing off, in the high-pressure, hustle-and-bustle life of a tournament deck? If so, keeping to the guidelines for event-legal alters may be a priority. Or is your alter instead going to find a comfortable, spacious home in a binder, in a casual Commander deck, or even framed on a wall? If you're not concerned about competitive players calling a judge every time your Liliana of the Veil hits the table - simply because she is now a squid monster with robot hands destroying a Smurf village- then we won't limit ourselves with rules that won't apply.
Serious or Silly?
If you follow me, you may have noticed that occasionally I go just a wee-bit off the rails. I do a really lot of alters. So when someone requests "something unique! Something you've never been asked to do! That nobody would think to ask for!" I warn them that it will indeed be unique - but may very well also crash through the boundaries of the bizarre, twisting and wringing the fibers of sanity until coherent thought is naught but a puddle of shimmery goo on a floor that does not exist. Or I might just draw a purple ladybug or something, you never know.
So it's important to specify if you have a preference on amount of sanity you'd like to retain in your alter. As with many of these choices, they exist on a spectrum. You can pick anything from "this would be right at home as an alternate printing of this card." all the way to "I need to hide this from people, or they'll send me back to the asylum."
Respectable or Irreverent?
If you alter were a movie poster, what rating would it get? Are we doing a family film that Disney would happily show at a nun convention? Or maybe it's a saucy movie that you might have to keep a few extra staff guarding the back door to keep teenagers from sneaking in? I like the movie poster analogy, because no matter the rating of the film, the posters are for all-audiences. And since I do these at public events, and post them all, and they get played, I alter to an all-audiences standard.
Do you have a theme?
Often, card alterations are enhancements or embellishments on a theme. Perhaps you collect vegetables that look like famous historical figures and preserve them in jars. You could add to that collection with similar card-alters. Perhaps you have a Commander deck that was modeled off of the movie "Grease." You could alter Kresh the Bloodbraided into a young John Travolta. Or Olivia Newton-John. Or a classic '57 Chevy that was secretly a Transformer, and, finally fed up with Kenickie and Rizzo's "dalliances" in his backseat, shows his true form and rampages through the quiet town, forever changing the course of humankind, shattering our trust of technology, and sparking an interstellar war that rages for centuries. Way to go, Kenickie and Rizzo.
Canonical or Concepty?
If your idea includes something that, more or less, already exists, you may want to consider just how true to the original you want to stay. Accuracy is neat - I'm a big fan of it in surgeons and snipers especially. But also neat, is to wander off the beaten path a bit, and see what that noise in the bushes is. You could catch a leprechaun over there. It could be there's a hidden portal to a universe where every living thing, even dogs and cats, fish and spiders, look like Chris Hemsworth. Also it rains Junior Mints there.