You can use the d20 System's existing magic rules to some degree as a baseline. 1 mana in MtG terms could be equivalent to one spell level's worth of Spell Points (
see the variant rules in the SRD here). Spell Points are essentially a conversion of the psionics "power point" costs to magic; just call Spell Points "mana" (though it must be noted that while a 1st-level spell costs 1 SP to cast, higher-level spells have their cost increase in 2-point increments; a 2nd-level spell costs 3 SP, a 3rd-level spell costs 5 SP, etc.).
Lightning Bolt? A 1st-level spell. The 3 damage might instead be 3d6 in D&D terms, to a single target (or maybe a 5-foot radius spread); sure, that's better than a Magic Missile or Burning Hands, but it doesn't scale up with level, so it isn't too overpowered (but really, Shock would be a better example of a 1st-level spell; 2d6 damage, no scaling). Summoning Grizzly Bears? A 2nd-level spell that summons maybe 1d2 black bears (1d2 is generally represented with a d4 roll, with rolls of 3 = 1 and 4 = 2), maybe just 1 bear, probably short duration (1 round per level or maybe just 2 rounds period? A Planeswalker would just be an epic-level character with a Planeswalker template, who would be using the equivalent of metamagic feats (Automatic Extend Spell or Automatic Persistent Spell) to make the summoning last longer). Etc.
Just keep in mind that Planeswalker casting times, spell effects, durations, and such are on a different scale from mortal spellcasters. Just bceause a spell or creature is "permanent" in MtG doesn't mean that it will be so when cast by a normal mage; only a Planeswalker likely has enough juice (in the form of metamagic feats and spell slots above 9th-level) to make a lot of spells permanent. A normal mage casting the same spells will just get a limited duration and lower effect (not all those epic spell-boosting feats and buffing spells and template benefits and whatnot).
Though even normal mages can cast some permanent spells; they're just weaker than the permanent spells a Planeswalker would toss around. And enchantments, for example, cast by normal mages would probably have a duration measured in rounds, aside from a rare few (for example, permanent light-producing spells are common in some places of MtG's settings, but they seem to require expensive material components or something to make them permanent, since they're only used in some richer places).
Using stuff from the SRD here, you would probably do well to apply Magic Ratings and Spell Points to emulate an MtG feel. Even non-casters should get Magic Ratings, though they do no good unless the character multiclasses into a spellcasting class (because everyone in MtG has a natural attunement to the mana around them, and the longer they live somewhere or whatever, the more mana gets attuned to them).
You can assign a color to each Spell Point (i.e. each point of mana); say that the PC chooses how much of their mana is of what color, but they should at least have visited an appropriate area beforehand. I.E. wizard A levels up and gets some new SP/mana, 3 points let's say; he has traveled through a marshland and spent some time in a big city since his last level, so maybe he chooses for 2 or his new mana to be Black and the last 1 to be White mana, or maybe he chooses for all 3 to be White mana, or whatever. Each spell would, of course, require mana of a particular color to cast (and some would require any kind of mana for part of their cost, as normal in MtG).
The standard Sorcerer, plus the
Battle Sorcerer variant can represent your spellcasters, while replacing their spell lists with MtG spell lists, but it's probably best to just make your own spellcasting classes that better fit the theme and whatnot. Probably a spellcasting scholar of some kind, a warrior-mage of some kind, and a warrior with just a bit of magic. Or you might very well just use the
Generic Classes from the SRD to simplify things, and it would fit to some extent. Though Barbarians, Rogues, and a few other classes would probably still be around as well. Note that the class-features-as-bonus-feats list in that section is ONLY for generic-class bonus feat options; other classes can't take those feats and nobody can take tham as normal feats for level advancement, they have to be taken as bonus feats from the generic classes, if they're taken at all.
Note that counterspelling in MtG requires particular spells made for that purpose. They don't necessarily require identifying the spell (some only work against particular types of spell, which would then require a Spellcraft check to identify it before countering) and they don't require a dispel check; they just work automatically when you cast them. Probably have a casting time of 1
immediate action, but note that if you use an immediate action on your own turn, it just uses up your swift action for that turn, so you could use another immediate action too, but it would use up your swift action for the next round (and that's the limit of how many you can use).
So no big counterspell wars would occur, but if you cast a standard-action spell for example, then your opponent tries to counter with an immediate-action Counterspell, and you counter his counter with an immediate-as-swift-action Arcane Denial, then you would still get your standard-action spell off without a problem, and could still cast your own Logic Knot or other counter on your opponent's turn when they cast something (but then you'd have no swift or immediate action left to use during your own next turn).
I'll post whatever I have in this vein later, if I get around to finishing any of it (I have a bunch of Kavu partially statted up, and will get around to statting up other MtG critters for D&D/d20 at some point). However, one important thing to note: if you try to make this project a for-profit thing, or even just to publish it freely as a PDF or something else, Wizards of the Coast WILL issue a Cease and Desist order on you if they notice (AFAIK they did that to Michael Morris' "Dusk" material that was around here some years ago, because he based it on MtG, though he did change it around some at least).