There's three major categories for Pokemon guidelines we follow here,
and whenever you design a Pokemon you need to include any combination of at least 2 of the 3.
Before getting into these three categories, I want to make sure something is clear:
For Pokemon that are normally upright (walk on 2 legs like a person) if you do not like bipedal Pokemon and want to design it on all four paws, that is perfectly fine. We don't class that as an "iconic trait", and regardless of what the Pokemon's Typing is - including if it's the canon Typing - your Pokemon can be on all fours if you prefer.
When discussing user-designed Pokemon and comparing them to the official Pokemon of the games and other media, official Pokemon will be referred to as CANON Pokemon. When something is canon, that means it's taken directly from source material that's established as fact in the fictional universe by the original creator(s).
I use Skitty in these guidelines, so here's an example of canon skitty and an Ice-Typed Skitty I designed, side by side:

With that out of the way, let's get to it!
The 3 categories used to assess a Pokemon design are as follows:
Iconic traits
Markings
Colors
Iconic Traits:
Certain traits are as much of a Pokemon's identity as its name is. The unique aspect of these traits are an essential part of recognizing the Pokemon. Stantler's antlers are designed in a way to imitate large eyes. Bulbasaur has a bulb on its back. Ponyta has a mane and tail of writhing flame.
When you design a Pokemon, it should always maintain at least one of these recognizeable traits. A Poison-Type Ponyta could have a mane and tail of visible "poison" gas. A Dark-Type Ponyta might have a mane and tail of billowing fog or black smoke. A Rock-Type Ponyta's mane could be a ridge of jagged stones colored separately from the rest of its body, and its tail could be a single stone (like when real horses have their tails cut down) or a bunch of large rocks, or maybe something different entirely - but it should still reflect the essence of that Ponyta's typing, just like the original Ponyta's mane and tail reflect its Fire typing.
With less popular pokemon, or just Pokemon of certain designs and certain Typings, it can be harder to spot exactly what would be considered an important trait on its body.
If you look at Skitty:

It doesn't exactly look remarkable right off the bat, it just looks like a pink kitten, right? Right. It's not exactly striking. However, even Skitty has a couple key traits that make it immediately recognizable. Besides the extremely skinny tail with the huge poof of pink fur at the end, a very important part of Skitty's design would be what I call the hat-pins on the end of its tail:

This is really noticeable, and no other cat Pokemon in the Pokemon universe has a tail like this. When you design your Skitty in otherTypings, it needs to have something on the tail hinting at this, whether it's the same thing in a different color, or your own unique turn on it. I have an example below:

I gave the tail more than three tufts, but I still hinted the original design by keeping them in groups of 3 - 3 on each side, and 3 different sizes, and 3 different points - you get the idea. You don't have to be that literal, and original designs can have more or less than three - but there has to be a clear, recognizable reference of the original design present, on the same body part as it is on the original design.
If you're doing the Pokemon by its canon design, you need to have the same literal element - so a canon Skitty would have to have three tufts on its tail. Exactly what you make them out of can be up to you, whether it's obviously fur, or…something else, but there have to be three of them.
Markings:
If you want to take liberties with your Pokemon's markings, that's okay, but they have to be in the same category as the original canon design - so if you want rosette leopard spots on a liepard, that's fine, as long as they're spots! If you want tiger striping on a Zebstrika, that's awesome, as long as they're stripes!
Pokemon with "iconic" markings should still have either the marking or a variation of the marking from the canon form on them. Liepards need to have spots of some kind, and Zebstrikas need to have stripes of some kind. Aside from that, many Pokemon with markings may have specific markings unique to them.
Skitty is a good example of this:

Skitty is a cute little cat-pokemon known for absolutely wrecking me with how cute it is. Look at its happy smile. Its little nose. Its little kitty forehead must be so soft. Oh my god.
Skitty has a semi-circle marking on its forehead. When you design your skitty(or other Pokemon!) they should make reference to specific markings like this. Here's an example of an Ice-Typing Skitty and its variation of the marking:

Whatever you decide to put in place of the original marking, you
can not completely remove the marking.
So your design of Skitty, whether it's a different Typing or just your interpretation of the canon design, it has to have something there. The same goes for the pink marking on its head and back - you can change the size, shape, edges, make the color darker or lighter,
but you can not remove it completely.
Colors:
Colors can be tricky when it comes to Pokemon Type Variants.