The most compatible fluids are Castrol LMA and ATE type 400. Both are DOT 3 or 4. Don't use DOT 5 - it's silicone-based and may create problems with seals. You will need about a pint of fluid total.
Since the front and rear brakes are separate systems, it doesn't matter which you do first. While you can use a vacuum bleeder, it's not necessary.
I would do the flush this way:
Open the right front bleeder and pump the brake pedal (slowly) until the reservoir is
almost dry. If you run it completely dry, you will be punished.
Fill the reservoir and pump the pedal again, until you're getting new fluid from the right caliper. (Obviously) Don't ever let the reservoir go dry!
Do the same process with the left front caliper.
Repeat the sequence with the rear calipers, doing the right one first, then the left.
The feed for the clutch is midway up the reservoir, so don't let the level fall below the feed hole when you flush the clutch. Have someone depress the clutch while you open the bleeder. Close the bleeder before they release the pedal. Repeat until the fluid is fresh.