As much of my playtime on Melee was Marth vs Roy (my main vs my brother's), we both developed very grab-happy playstyles since that's the one thing Counter wouldn't kill us for. That said, here are a few tips:
- Try repositioning yourself while landing. If they're grabbing you as you land, it means you landed right in front of them, or they predicted your landing spot. Different characters have different falling speeds and horizontal mobility, but trying to swap that up can make you harder to predict.
- Alternately, remember that grabs do not have armor on them in this game, so you can beat a grab with an attack. This depends on your character of course, but if you can force them to at least take some damage in exchange for their grab, go for it. Bowser Jr can cover his landing somewhat decently with Mechakoopas or the exploding kart from UpB, for instance. Down-air is also a good move for a lot of characters, just be wary of your timing and the landing lag you're subjecting yourself to.
- And of course, if you're running into this as a result of the opponent waiting and shielding, instead of charging right in, try harassing them out of their shield. Going by your avatar block, Olimar and Bowser Jr are both pretty good at this, as they have several projectiles to use to coax them out. Other characters like DK would be better off using a move that will heavily damage or break the shield, like SideB. Characters with neither option should save double jumps for escaping after faking out.
As for rolling and dodging, rolling is just as punishable as spotdodging if not moreso, just in different ways. The key is to use them, like any other move, unpredictably in order to avoid getting punished for it.
Positioning is really important, of course, and with a lot of the changes to dodging and aerials, the ground game in particular has become stronger than it used to be when compared to air. It can be very hard to land, but learning to do so well will give you an advantage. One last consideration, if you're near an edge, consider going straight for the ledge since that will give you invulnerability for a moment.