Falcon Six Performance handbook mandatory aftermarket option.
I'd strongly suggest setting a slower timetable, and make every goal post a winner. 3 grand is not enough.
The enemies of sucess are
1)the modifications needed to fit any carb better than the stock 1-bbl height,
2) the piston issue (intimated below),
3) and the ability to restrain yourslef from creating 'just' a 165 hp net engine.
The 250 is very strong, fairly compact, and its built in design 'faults' are easily fixable without machining the block down, or having to find 12 cc dish pistons. Due to the thinwall deck of log head blocks, it is sometimes a moderate risk to deck the block down more than 50 thou from the stock 9.469 deck register on any of the 250 Ford sixes.
(The piston edges park short about 103 to 110 thoufrom the top of the block, the centre of the piston about 300 thou, so there is a huge loss on the ideal combustion chamber for good performance. Aledgedly, the large exposed heat region creates detonation, dieseling, running on. Finding a way to raise the piston up in the block without milling the deck should be the primary goal.).
On a budget, I'd suggest
1)a set of stock 5.88" forged steel rods,
2) and six 255 Ford 4.2 Liter pistons.
3) Deck the block from nothing (0) to 50 thou, no more. Compression will be quite high,
3)Use a rebuilt D8 code head with a nominal 60 to 62 cc chamber should allow it to work okay.
4) You should do the direct mount 2300 Holley modifications as per the Handbook, but it'll take time and money to get it to work with a 2-bbl Holley, so I'd suggest you stick with a 1-bbl carb, and just make mount a Torco 1-bbl to 2-bbl adaptor from Summit upside down to allow you timne to source a cheap 2300 carb latter. There are some good 1-bbl Ford carbs around, and you could waste 500 bucks and add a lot of frustations to simple project.
5) A good cam (264 degree) and a good big emissions era 1-bbl 250 carb from a 4.1 liter Granada or 300 F150 truck should help,
6) a great ignition system tuned for mean best torque,
7)port divider
8) headers,
9) a proper, modern AOD or RUC or SROD or V8 T5 gearbox (each has perfect ratios) will have your budget truly spent.
10) With a set of 3.25:1 gears, you'll love the results. 3.00:1 stock gears will suffice, but any 250 Ford engine has a sensational amount of low end urge for the first 60 feet off line, quite unlike any V8. Anything more savage than the stock 3 or 2.75 gears is to be recomended. I had a lot of fun with a 3-speed and 2.77:1 gears in my 250 Falcon, but a great spread of ratios is the single best thing to do, even above better carburation.
Form sedan racing experience, a 1-bbl carb with 215 cfm at 3" Hg should give 165 hp, it does in Australian 3.3 liter engines reworked to this spec.
11) When circumstances allow, go to the 2-bbl 2300 carb with a compact Does 10's style remote carb extension. It will fit.