You can't go by color alone, you have to understand what the wires do. Here's what happened when you hooked all the like-colors together. BOOM.

This is probably how it was connected originally. However, this is wrong and illegal, for several reasons: white wires must be neutral unless marked otherwise, and here it's a hot mess. Also, "hot" is always connected to the light fixtures even with the switch off, which can surprise the guy working on the fixture. It's also likely that the white wires on the fixtures are actually "hot" - that's especially dangerous with Edison style sockets.

Here are the exact same wires, rearranged in a way which is legal and solves all of the above problems. Now the "hot" wire to the fixture (red) is switched, and neutral is always connected. With the switch off, the fixtures see no power. Note it now matters which end the switch is on, because on one end, white is actual-neutral, and on the other, it is switched-hot.

On the right of this drawing is called a switch loop. Those are wired with black-white cable out of sheer practicality... the white is not neutral, but is switched-hot. Legally the wire must be marked, typically with a few wraps of electrical tape. Black will suffice, use red if you have it.

This switch loop arrangement is actually obsolete. In new work, code now requires neutral be brought on switch loops. In that case, all 3 wires would be extended to the switch, and neutral would not be used until the happy day you get a smart switch or motion sensor.

The color of the wire-nuts do not matter, as long as they fit the wires - they have a lot of range. Yellow is best suited for all the connections here.

All these drawings omit ground wires. That's commonly done on illustrations like this. Nonetheless, all the grounds do need to be there and be hooked up.

One last thing: You'll get way less light. A dual 4-foot fluorescent (62-90 watts) produces the same light as 400-500 watts of tungsten bulbs. If you hate the fluorescent flicker, lousy cold-start or hum, or the ballast or starter has failed - electronic ballasts fix all that! And you can retrofit your existing fixtures. If you hate the fluorescent color, they fixed that too - tubes and LEDs now come in excellent color rendering (80-90 CRI) in 3000, 3500, 4000 or 5000k color.

You can go T12, T8 or LED, and 2, 3 or 4 lamps. That is decided by which ballast you buy.

Instant, or Rapid/Programmed Start.

This is decided by the wiring of your fixture. Each bulb end has 2 pins because there's a small filament in each end of the bulb. Rapid or Programmed Start ballasts use both pins to preheat those filaments for an easy start and longer lamp life - so they have 2 wires to each end of each bulb. Instant start ballasts do not, so they only have 1 wire. If you have instant-start, stay with it - otherwise you may need to replace the lamp sockets.

T12 vs T8 vs LED

You probably have inventory of T12 bulbs, but they are basically obsolete. T8 bulbs are inexpensive, more efficient, have much better color rendition (typically starting at 80% CRI) and come in several light colors (3500K, 5100K etc.) Edit: since I wrote this I have started fitting 90CRI T8 tubes, readily available for under $2 each, they are marvelous. You don't see it in the tubes, but rather, in the stuff being lit up.

LEDs come in 2 flavors: "direct wire" (rewire the fixture for 120V on the lamp ends) or "keep the ballast". (no rewiring, the smarter LED emulates a bulb). The trouble with the second kind is you must maintain the ballast, and it must be of a certain type (i.e. instant start). With direct wire, you remove the ballast entirely and wire 120V to the lamp end(s). Some "direct wire" LEDs take the 120V on one end of the lamp (the other end is a dummy) - that can be a problem in a fixture with 1-wire sockets.

2, 3 or 4 bulbs

T8 bulbs are generally brighter than T12 bulbs. Look at the bulb rating in lumens, but multiply by the ballast factor (a percentage) - they make ballasts designed to underdrive or even overdrive the bulb's rating. Often when lighting is carefully designed, they replace 4 bulbs with 3 or 2, because T8's are brighter and/or because they found the space was "over-lit".

LED lumens are lower, but they're worth a lot more, because they're all aimed in the right direction - unlike fluorescents which waste a lot of energy lighting the backside of a reflector.

Sourcing

Changing ballasts is rather straightforward and I pay between $12 and $30 on 1000bulbs.com or other sources. I aim for middle to top shelf quality - my first choice is GE, and I find good deals on boxes of new ballasts on eBay. Edit: 4-lamp ballasts are readily available. The tactic of getting 3-lamp ballasts and only fitting 3 tubes works well with T8, as they are somewhat brighter.

I have also been doing great on eBay buying new or lightly used ballasts that were pulled from newish fixtures for LED upgrades. As low as $4 each.

I regularly see direct-wire LED replacement 4 foot "tubes" for under $10, often from 1000bulbs.com or superbrightLEDs.com.

It's pretty easy work if you don't mess with the lamp sockets - just get a big bag of "blue" wire-nuts, a stripper, and go to town. If your fixture is hard-wired, you must install "disconnecting means" - I power down, install half the connector on the hot lines, then power up and do everything else.

When I replace lamp socket ends ("tombstones"), I pay about 60-70 cents each for those, and they are fairly standard. But the labor gets pretty high.