How would you build a low 10’s street car

Okay, I am building a 67 Valiant that I hope to get into the low tens or maybe even high 9's with, and I know what I've done, and what things are costing, so I might be able to give you some real world perspective. My car is being built to the NHRA rulebook, and is fundamentally a race car. I will occasionally drive it on the street, but it's a race car first. Probably the first thing I'll tell you isn't something you want to hear. Any older modified car that runs 10 second 1/4 miles, is not going to be a very streetable vehicle. The modifications needed to the chassis, suspension, and drivetrain will make it a bit of a handful on the street. Either accept that now, or build a nice 12 second car, which is way more fun on the street anyway. Most people who haven't been in one don't seem to understand how much difference there is between a mid 12 second car and a mid 10 second car. It's night and day, chalk and cheese.

First of all, to achieve your 10 second performance goals, you need to focus on several things that are not engine related. A ten second car is going to reach 130+ mph in the lights, so it needs to be safe. A roll cage should be a very high priority item.
Serious brakes. Don't even think of retaining any part of the cars original braking system, it all needs to be upgraded.
Traction. You can have all the horsepower in the world and it won't do you any good if you can't get the car to hook up. This means wider tires than will currently fit on the car, narrowed axle, wheel tubs, and likely a completely new style of rear suspension. (my car uses a narrowed Ford 9" with a 4-link, and adjustable coil overs) And if you want to run 10's you will need slicks, which you can't run on the street, so that means two sets of rear wheels and tires.
Chassis stiffening. You want the car to transfer weight when you accelerate, so you will need to stiffen the chassis. Think frame connectors, torque boxes and again, a strong roll cage.
Weight. The lighter the car is, the quicker it will accelerate. You should try to get the car under 3000 pounds fully equipped ready to race. This means foregoing the usual niceties in a street car... no AC, power accessories, no carpet, no fancy upholstery, etc. Suddenly it's not as inviting a place to be, especially if you want to drive it on the street regularly.
Drivetrain. To get a 3000 pound car in the tens is going to mean 550 to 600 horsepower. Now you need a convertor, transmission, driveshaft, engine mounts, cooling system, and fuel system to support that motor. Unless your name is Dick Landy or Ronnie Sox don't even consider a manual transmission.
Money. As other have pointed out, speed costs money, and the faster you want to go, the costs climb exponentially. Paying people to build the car will easily double the final cost.
Here are some of the costs I have incurred while building mine, doing all the work myself except for building the engine and trans.
Roll cage - 650
Racing seats - 700
Fibreglass bumpers - 450
Sandblasting and epoxy undercoat - 2500
Gerst K member - 3700
S&W back half kit - 1800
9" narrowed rear - 3200
Baer Brakes - 1800
Strange shocks - 550
Fuel cell, pump, regulator, lines, - 1500.
720 HP naturally aspirated engine - 19,800
Trans and convertor - 3300
Wheels and tires - 2000

As you can see, I have almost 40 grand into the project and it's not painted, wired, plumbed, or cooled yet. I fully expect to spend another 15 grand before it's done. Perhaps these facts will help you adjust your goals, or just make you start saving money. Either way, have fun with it!