I just bought a 79 Pontiac Trans Am with a 403 in it and I am looking for recommendations for a mild street build, my budget is in the 1-2k range and I don't necessarily want to deal with a machine shop. The block is fine and doesn't need anything besides a dingleberry hone. Just want some recommendations for decent street performance.

 

Your factory heads suck with large chambers. Early 330/350 heads with an upgraded cam, headers and dual exhaust. You need a higher stall converter with a bigger cam. Honestly a built 2004R and 3.73 gears would add the most fun.

 

Your budget is the limit, by far. The biggest limitation on the stock 403 is the heads; especially the exhaust port. You can port them yourself and get them similar to earlier heads, but it takes a lot of time. And unless you've done that a lot you'll probably hit something which means going to the machine shop to fix it. A few things are pretty simple, like grinding out the AIR bumps.
Cam, headers, exhaust and converter and you're probably at your budget. If you can find early heads for cheap - ready to run, because refreshing a set of iron heads costs almost as much as a new set of heads - then those really help. The bolt holes have to be opened up to 1/2" though. Easy to do but you do want the holes to be straight!

Raising compression is a big help. You can use the stock pistons with early small block heads and get in the 9's (IIRC); or use big block heads (aftermarket or OEM) along with flat top pistons. Sticking with the stock heads and pistons means really impacts cam choice.

 

I have 2 stock short block 403 I built up running in my el Camino and cutlass. I got one in good running condition out of a 77 Buick in the junk yard and ran it completely stock for a while. I inspected bearings and cylinder was and was happy so I did gaskets,
224 @ 0.050, .540” lift single pattern cam
double roller chain
roller rockers(hardened pushrods)
#7 heads with 2.07 1.71 valves and crossover filled
performer rpm intake and quadrajet
I did my math wrong and had the heads cut to much so it’s about 9.75:1 compression but I was able to make it run on pump gas. It runs surprisingly hard and is actually more engine than I meant to build for the car.

The 403 in my 67( currently not in) is factory short block with gaskets
228/238 @ 0.050 .509/.498 lift
cloyes stock replacement timing chain
stock style rockers
4a heads
performer rpm intake with quadrajet
the stock heads plus fel pro permatorque gaskets equal sub 8:1 compression so though it runs well it is not fast by any means but compression and better heads should really wake it up. I had almost all these parts in the garage already so I can’t give a good idea on costs but if you buy used and wait for deals you can build a healthy 403 fairly cheap.

 

Biggest issue with the 403 is compression. Early heads, #2, #3 will need the pushrod holes wallowed out a little bit with a tapered drill bit because the camshaft bank angle is 45* instead of 39*. Can be done with a hand drill, doesn't need to be precise. I suggest 330 heads because your budget. will need to be cut .030 to make up for the inexpensive but thicker (.024" thicker) Fel Pro replacement gasket (stock pistons yields ~9.1:1 compression). Can get inexpensive stainless valves from Speedmaster. Or pop the valves out of the 4A heads you have if you really can't bust out the $100. Don't cheap out on springs. Can reuse your locks and retainers but Edelbrock 1.437" run like, $100. Need to have the head bolt holes drilled precisely to 17/32 for the 1/2" head bolts and the block dowel hole needs to be drilled to 5/16 (?). Mark can chime in on a cam but can probably get away with an Erson TQ40. Reuse your pushrods, they'll be fine with pedestal mount rockers but not guideplates so factor that into your planning/budget.

Edelbrock RPM intake, roller tip rockers or Ford Pedestal mounts can be found easily. eBay long tube headers.

The recipe above will get you close to your budget and over 300hp to the wheels.