A few quick thoughts (sorry this isn't more complete but I'm in a hurry):
FIRST, make sure you can take-apart the existing system, particularly the pieces you want may need to keep (e.g., the evaporator). Seriously, you may find there are fittings that are virtually impossible to loosen without damage.
The HT6 is a notorious leaker. Check yours and see if it feels oily or shows other evidence of oil around the underside.
Consider a Sanden #4440 replacement instead of another HT6, if replacement is desired.
I just "rent" a vacuum pump from O'Reilly or AutoZone.
Get plenty of vacuum oil for the pump (I get it on Amazon, 32oz bottle; it's more expensive at the stores). I've almost always had to change the oil in the vacuum pump at least once every time I use one (it takes maybe 8oz) to get it to draw to 30" of vacuum. When the oil is contaminated, the pump won't pull full vacuum. Get oil.
Hook the gauges to the vacuum pump (just to the pump, not to the AC system yet) to check them both before you use them. Make sure you can pull 30" of vacuum. If not, try changing the oil in the pump and / or check your gauges for a leak (I've had both problems haunt me... needed an oil change on the pump and a replacement O-ring on the high-side valve of my gauge set). Tap your gauges from time to time (a rap with your knuckle, a tap with a wrench) when you read them, as I've had gauges get "sticky" and not read correctly.
Flushing the condenser is IMHO a bad idea, the passages can be too narrow to effectively flush (the old tube and fin condensers of the R12 era perhaps, but not the narrow-tube R134a condensers).
Pull the orifice tube. If the screen is clean, then consider skipping any flush...
consider. There may be other reasons to flush, e.g., to purge the system of old oil if you believe the system's had an opportunity to take on moisture (via a leak in the system) or if you simply want to start from "clean" to get the oil volume correct in your (new-ish) AC system.
If the orifice tube screen is dirty or plugged... I'm not sure what to say. I would replace *everything* upstream (including condenser, which is relatively easy on the GMT400... the radiator can stay in place) and all hoses (easy) and receiver-dryer (which you would replace anyway). The evaporator would be tough to replace. I might try flushing it separately (with all hoses disconnected) and monitoring the outwash for debris. If it seems to flush clean, consider leaving it; if there's evidence of debris... I can't recommend keeping it
When I've used flush, I've used a high-volatility liquid flush like Four Seasons 69994 Super Flush or JOHNSENS 6544. The low-vol flushes are more akin to mineral oil in volatility and thus harder to remove using vacuum. High-vol flushes are flammable(!) so use them with care.
Get new valves for the service fittings. There are two different valves used on the service ports. One of them uses a simple, replaceable Schrader valve (obtain from NAPA). You may need a special, deeper-reach tool to remove / replace the Schrader valve (I have one that I bought from... somewhere). The other valve is integral to the fitting (search for GPD 5811340), and the fitting can be replaced with a couple of wrenches (one to turn the fitting, one to use as a backup wrench to hold the manifold).
Read-up elsewhere on how to vacuum the system. It should hold vacuum overnight and longer, if the system's tight and your gauge set doesn't leak(!).
When ready to fill, i.e., with the system at 30" vacuum, engine off, both gauge set hoses connected to their respective service ports, BOTH valves CLOSED on the gauge set, I typically fill through the high-side port with liquid R-134a (i.e., invert the can, open the high-side valve) until I'm getting close to system capacity (say 90%... but it may not accept that much, don't fret if it doesn't). Then I'll CLOSE the high side valve on the gauges and start the AC (engine on, AC on) to draw the pressure down on the high side and pull the remaining liquid from the gauge's high-side hose. All the while, I'll watch / check pressures on both high and low sides. If they look good (they always have, for me) I'll set the R134a can upright so it's feeding ONLY vapor, and OPEN the low-side valve SLOWLY (because there may still be liquid in the hose between the can and the gauge set, and you don't want to dump that liquid into the low side right at the compressor!) to admit vapor into the system. I'll then let system run like this (AC on, etc., low-side valve open, can upright dispensing vapor) until the desired volume of R134a has been installed.
I use a 30# can of R134a and sit it on a digital scale, so I can measure the amount of refrigerant taken from the can. A person can get along with the 12oz cans and no scale, but having a scale is definitely handy in every situation.
Don't get cute and overfill the system, e.g., as a buffer against future leakage. If you do the high-side cutout switch will start "cycling" the compressor when, e.g., you're sitting at stoplights in the heat with the AC on (or in other situations which can lead to high head pressures). Been there, done that. Nothing is more humbling than having your wife sweaty and unhappy after you've insisted on servicing your AC yourself
There's much more to say, but what I've posted will get you going and probably generate more dialog in this thread.
Let's see what others have to say.