He is asking about a road coarse car... Wow jump to conclusions much?
Assuming you're asking about a road race or autocross car, I think I can try and help
In short
You can't be competitive in both cornering and acceleration for that budget when your foundation is a Dart.
You will get beat by every Evo, STI, Turbo Civic
. The list goes on.
This isn't entirely true. If your Dart is already a solid car (ie, the entire 10k goes to mods/upgrades, not floorboards) and you have some mechanical/fabrication skill, $10k will go a long way. You can have a Dart that should be able to pull a lateral G if you do it right. Now, will you compete head to head with Evo's and STI's? Probably not.
But it depends on if we're talking autocross or road racing. Autocross is hard even for A bodies because they're big, and autocross courses are not. Road racing is a little different.
Anyway, this is what I'd do...
Suspension-
Front end rebuild kit with poly bushings $500 from Just Suspension
1" Torsion bars $200 from Just Suspension
Addco 596/675 Sway bars (F/R) $300 from Summit
RCD Shocks $400 from Hotchkis
Frame connectors (2x3" steel) $100 if you can weld
"Road Race" leaf springs $260 from Firm Feel
Boxing plates for LCA's
Wheels & tires
15x8 or 17x8, 245/255 series all around. Price depends on what you get, anywhere from ~$1200 for cheap steelies and good tires, or a lot more depending on rim selection.
This will get you in the handling ball park. Because you already have a '73, you could also upgrade to later 11 3/4" disk brakes up front, probably for around $300. You need new disks and the 11 3/4" caliper brackets. Find the right brackets and you can keep your calipers. The disks come off of 77-81 Cordoba's (and similar, Diplomats etc). Nice, but not absolutely needed.
This would get you started with good handling car, with the right tires and tuning, you could probably approach 1 G on a later skid pad. You'd probably also need offset UCA bushings to get your alignment right, set it up with -1/2 to -1 degree of camber, and in the neighborhood of +4 degrees caster. If you bought everything, (brakes included), you're probably in about $3,500 if you spent wisely.
Engine-
Assuming you've got a 318, you can get 300 hp out of a fairly mild rebuild. Flat top pistons, near 10:1 on the compression, larger valves in 318 heads, or maybe 302 heads or a set of magnum heads. Get in the 300-350 hp range, with good gear selection, and you'll accelerate fine. Even more toward the 350 hp mark, you should be able to do this for under $4k, even if you don't do the work yourself.
Should be money left over. Adjustable UCA's are nice, but if you're racing be careful, that could put you in a different bracket. You can also look into steering, a rebuilt manual or power steering box will really help. You can drop $500 there pretty fast.
By no means the "end all, be all". But do that and you'll have a pretty quick Dart that will handle well.
Be sure to look into rules for racing organizations you want to participate in, you don't want to put yourself in some kind of modified class and get your butt handed to you. You may need to stay away from tubular UCA's as I mentioned, but also through-the-floor type subframe connectors. They also have rules on tire sizes and tread compounds, so you'll want to look into that when sizing your rims/tires.
Find AutoXcuda on here. He's well versed in this. And do a search!