For challenge purposes any K plus boost is sweet.
k20a3 base rsx and 02-05 Civic SI have weenie little rods that break around 400hp avoid except for oil pumps and sweet steel oil pans.
K24A1, K24A3, K24A4, K24A8 are all damn near free ways to the platform, emissions focused intake cam only vtec, lowish compression, and limited vtc angle make them forgiving to tune.
K24A is a mess. The engine designation for all JDM 2.4s some are functionally identical to a K24A1, K24A2, or K24A4. Unless they are really really cheap I avoid completely, too many bad importers, too many ways for it to be a headache.
K24A2 is the TSX engine 02-05 pretty sweet and very strong. 06-08 more compression, more valve, better intake, better cams, etc. If you want a reliable 500hp for a challenge budget this engine will do it. If you want pretty reliable 600hp this will do it. The turbo and fuel system to get to 700hp is tricky to put together for the $1000 you'll have left after buying one but done carefully a 700hp junkyard 4cyl that's not totally a grenade with the pin pulled can be put together within the challenge budget.
A basic t3/t4 hybrid and crappy manifold will get you to mid 300s on a CR-V engine at between 10-15psi.
The problem of turbo Hondas at the challenge is nobody buys injectors, the stock injectors can't do boost. Buy something in the 450-650cc range and turn base pressure down to get it to idle, 11.5:1 idle won't foul plugs too quick. Get a rising rate regulator in line to get pressure up in boost. It's not elegant but it would work.
If you can find one and AEM FIC might do the tuning trick.
Build it badass enough and you know a guy who has $200 in an AEM series 1 K ECU
As with all turbo Honda challenge cars free tuning is on me at or before the event.