You've definitely inspired me. It might be time to build some budget decks myself. I've been on an expensive bling kick lately, and I need to cool off and shift gears. Finding good budget cards does indeed present a much more interesting deckbuilding challenge. I tend to choose battlecruiser commanders that require A LOT of support from the deck itself to be competetive. Gishath, Niv, Aurelia, and Prossh were all the opposite of a budget commander choice. I found myself sinking more and more cash into the decks just to keep up.
Looking through the possible commanders I think I've found a bunch I would enjoy building on a budget personally that might even be competitive enough for my playgroup. 2 color decks are A LOT easier to build on a budget for sure since you don't have to worry about dual lands nearly as much.
These decks are decks I could sell to my LGS for players looking to get into commander, or just sell them directly I guess. I've encountered a few people interested in commander that don't have their own decks yet. I would choose commanders that someone could grow into and upgrade as their budget allowed. A starting point.
I think I'd elect to go for an overall deck value rather than single card value for my purposes. I can see there being a few things that really want to be in the deck but are over $1. You can make up that higher price tag in the rest of the deck.
Personally, I would pick commanders with built in card advantage and/or ramp at an efficient cost (4cmc or less) since it will help the deck be a bit more consistent if you aren't running all the expensive draw/ramp staples. I find these commanders to be A LOT less frustrating to play on a budget, especially for newer players.
If all of your decks are on a similar power level I wouldn't worry about choosing commanders that are "too strong" since they are meant to be played together. You want to be getting as much value from the command zone as possible. And inevitably, you will find yourself playing against more powerful non-budget decks and your commander will give you a bit of a leg up.
I know you are just doing dual colored decks, but if you ever do tricolor,
Henzie "Toolbox" Torre fits the bill for me. He's an excellant enabler and encourages running non staples with higher cmcs. For example
Timeless Witness instead of
Eternal Witness. You've got built in cost reduction, haste, and draw all for just 3 mana.
Azorius: Vega, the Watcher low cmc, with built in draw. This commander encourages running a lot of unique non-staplish cards.
Shorikai, Genesis Engine doing vehicle tribal with this guy seems like fun and would be a unique deck for your collection.
Dimir: Kels, Fight Fixer yup, i can get behind this one for sure.
Wilhelt, the Rotcleaver pretty obvious choice, but overdone. I've always had an itch to build a zombie deck.
Sygg, River Cutthroat an old classic. notably this was updated to indicate
"At the beginning of EACH end step..." Jon Irenicus, Shattered One this is the hipster dimir card. interesting build around
Rakdos: Mahadi, Emporium Masterramp in the command zone for 3 mana. I think I would enjoy building this commander.
Prosper, Tome-Bound an obviously powerful commander. Probably too powerful and overdone for your taste but I think building him on a budget would be fun and easy personally.
Gruul: Tovolar, Dire Overlord at least one tribal deck would be fun. lots of wolfs and werewolves on budget.
Neyith of the Dire Hunt nice classic aggro deck.
Faldorn, Dread Wolf Herald again, fun to build on a budget I think.
Selesnya::
Sythis, Harvest's Hand is a pretty obvious choice for me albeit boring.
Selvala, Explorer Returned leaves a bit more flexibility in what you can do with the deck. Probably overdone at this point but she's a fun commander IMO.
Gluntch, the Bestower is something I would probably enjoy. Very non-threatening and an easy way to make allies.
Orzhov: Breena, the Demagogue A very experienced player has a budget breena deck and I can tell you it is quite competetive. Fun commander for sure.
Nalia de'Arnise besides the sexy art, I really like her abilities.
Tymna the Weaver will always be a competetive choice. for some reason I was thinking she was cheaper, so nvm.
Izzet: Rielle, the Everwise so easy to find good discard outlets in these colors.
Eruth, Tormented Prophet pretty straightforward and gives you a lot of freedom to build.
Jori En, Ruin Diver really a flawless choice.
Golgari: Carth the Lion piqued my interest when he was spoiled. I think this would be a fun deck, but I'm not sure how many budget walkers there are in these colors.
Glissa, the Traitor another commander I've always wanted to build. So many cheap or free artifacts that can be looped.
Baba Lysaga, Night Witch classic aristocrat reanimator
Boros: Feather, the Redeemed probably my first choice also, because there are so many cheap cantrips that can be used for draw. I would consider her ability to be built in card advantage and it's a fairly unique deck for Boros colors.
Akiri, Fearless Voyager classic boros equipment.
Simic: Kumena, Tyrant of Orazca yes, Im a sucker for tribal.
Lonis, Cryptozoologist pretty interesting ability. You've got 2 sources of card advantage.
Zimone, Quandrix Prodigy I think I might choose this over
Gretchen Titchwillow. They are doing very similar things, but Zimone is usable earlier.
Well, that's all I got for now!
Side note: I think it would be neat to compile a list of viable budget cards for each category, draw, removal, ramp, etc... cards that are efficient and get the job done but are still $1 or less.