Hello Fella,
For not breaking the bank i always recommend playing more basics even in 3 colors i play atleast 18 in non grenn ones and 21+ in green ones
And personally i think in your list you could play with a big amount of basics cause you are very much focused on one main color Red. And so i would recommand you if you want to try around 18 basics
like 9-10 Mountains, 4-5 Plains, 4 Islands (ofcourse think about if you got mono colored utility lands aswell, than remove one basic of that color)
And for the rest, run basic fetches, evolving wilds, terramorphic expanse or my favorite Perilous Lanscape (very good)
Than fill up the rest with your 3 color tapped triome and dual lands but focus on including many duals that contain red as one color and not that many that share blue and white cause that color your also getting a lot through your mana rocks
so yeah i hope that helped a bit and remember i am no professional (just a chilled guy building 60§ bdget decks). But this recipe works for me and my decks always work quite well!
With that have a good on fella and let me know if it helped (I would love to know)
~Lawrence