Hydraulic Flat Tappet Camshafts, LA blocks

Of course on a tight budget...What would you do?

-3600 pound car, 2.76 gears, manual transmission, 360, going for daily driver.
What would I do?
Well in your case, with the block on the table;
The first thing I'd do is figure out if I can afford some quench-type heads, and high-compression pistons.

But if no, heads are out, then; how am I gonna get this thing to run detonation-free, at higher than the factory paltry 130/140psi (sealevel) cranking cylinder pressure.

And once I get to too much pressure (hard to do with open-chamber heads), then I can think about a cam kit.

The biggest hinderance to your car, is the combination of 3600 pounds plus the 2.76 gears. As for the weight, you can't do much about that. But it takes a lotta lotta torque to pull a starter gear of 2.76 x 2.66= 7.34, with any kind of performance. (which is almost like starting in Second gear with 3.73 x 1.92= 7.16).
Now; torque at idle, which your combo is gonna need, comes from cylinder pressure. and
A bigger than stock cam, with a later than stock intake closing angle, will only make less pressure, with no other changes.

Now, if you're NOT planning on headers, then you can advance the crap out of the stock cam, and pick up maybe 10 psi, in the stock engine, but at the expense of high-rpm power, which with 2.76 gears, and a dead overlap period, you don't need to care about anyway.
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Just so you know, in the past, I have installed that 360 2bbl cam into a lo-compression 4bbl-318, heavily advanced, with 2.76 gears, but with the A833od; and it ran really well, with 5500rpm valve-springs. The key in that combo was the 3.09 x 2.76= 8.53 starter gear (also in a ~3600 pound car.) That's 16% more than your 7.34, and makes the 318 feel just about that much bigger..
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Honestly tho, a low-pressure engine needs a starter gear closer to 10:1, like
3.73 x 2.66= 9.92 if a 360, or
3.91 x 2.66=10.40 if a 318.
Or
grab a 3.09 Commando trans, @
3.23 x 3.09= 9.98
2.94 x 3.09= 9.08
2.76 x 3.09= 8.53
All that gear-multiplication monkey-business can be avoided with either more cubic inches, less vehicle weight, or more cylinder pressure.
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And your car, depending on the year of the trans, could easily have the close ratio trans in it, with a 2.47 first gear, making the starter gear even lower at
2.76 x 2.47= 6.82 which is identical to my SECOND gear of
3.55 x 1.92= 6.82
This is not good :(