Cool! There are so many fun budget decks running around at the moment, but I wouldn’t suggest anything that requires a lot of set up, as set up means Tapu Lele, and Tapu Lele means not so budget. If you wanted to play Expanded, Rayquaza/Eelektrik is phenomenal and no card in that deck individually costs more than 3 of your dollars. Also, Aerodactyl/Talonflame is insanely good fun, and Waterbox is cute if you like systematic destruction. Carbink BREAK toolbox is fun and consistent too, but for me the best Expanded budget deck is Mega Manectric. It really requires very little set up and generally sits there taking 2HKOs with Turbo Bolt while not requiring much else. You can use Unown AOR instead of Shaybae and Leybae in that deck and often runs powerful item based consistency cards such as Trainers’ Mail and Acro Bike: much like Vespiquen you rip through your deck on turn one and sit pretty for the rest of the game. BTW, do not be fooled into thinking that Vespiquen is budget: it needs to spam Shaybae to work.
Standard is a bit more limited: Volcanion-EX is my personal favourite build. I am currently building it and it doesn’t cost more than about 85-90 dollars sans Lele. Also, Quad Lapras and Quad Sylveon if you like Crushing Hammering away at people’s souls ($80) and a brain child of mine: Invincikoko, has been good in testing on PTCGO (Quad Tapu Koko-GX with 4 Acerola and 4 Super Scoop Up etc.) and doesn’t require Leles.