The best budget decks are the ones you brew yourself.
Doing one color can make the mana base reasonable, 2 colors is bad and 3 colors is just terrible.
Also, certain cards are modern stables and thus more expensive than others.
In modern, you can brew almost anything from a list of stables and it would probably work.
Going outside these, you have to factor in a ton of things, especially how small your friend group is and what they are playing.
If your friends are like mine, then they bring a new tier 1 deck every week, so adjusting for their decks is pointless.
Here is a good base if you are in doubt how to brew your own stuff:
Black means you can include a discard package, do that unless you really are struggling for room.
Red means you can include a burn/removal package.
Blue means you can include a counter package.
Which counterspells depends on your deck.
Now look at the list again, which color can you afford to remove?