Okay...this is just me.
First, you need need to match your stain and finish. Everything used and done will affect the final appearance. Start by getting a 12' section of any old pine molding you'll be using. You will need some experimetal stock. I'm assuming you are buying molding and finishing/installing yourselves?
Buy the best pine molding money can buy. Go to a lumber yard and look their inventory over. An employee can assist you to answer questions or point the way. These moldings can come in 16' lengths, be preapred to get them home safely. Hire them...
The more running surface you can cover with as few pieces of molding, is the desired result. Make a list of what you need, including height, length of molding. Over buy by about 20%
Look at every piece before you buy. You want the top edge to be as straight as it can be. A 16' piece of molding is going to bend and wobble a little...just look it over for nicks, abrasions, split ends,etc. You are going to sand it ALL before you finish it, so now is the time to be fussy about all you are going to buy and take home.
Now it's time to store it properly so you can deal with it at your leisure. (Have I mentioned how much work this whole thing is yet?)
The best environment for it to be in would be the house where it will end up. You will need about 3 sawhorses of equal height to work on your moldings. When you finish them, you will want them to stay undisturbed for long hours at a time.
Oh, save yourself a lot of hassle and get the stain professionally mixed. If Menards doesn't custom color...go to Sherwin Williams...they will. Minwax is fine for what you are going to do. Buy a gallon or two and a bunch of plastic pails with handles. Go to an automotive store/Walmart and buy 4 car wash mittens...just cheap ones. A few pair of latex gloves is a good idea also.
More on staining later.
Pine blotching. Yup, it is some of the worst and it looks like hell on molding. The easiset, care free method I have tried lately to remedy blotching came from the website of Bri Wax. I made some pine lap desks for Christmas and wanted them to appear old without too much work. The site suggested using a 50% solution of both water and a Liquid Plumber type drain cleaner. I experimented on some scrap baseboard and it worked better than anything else, short of spraying with a spitcoat of shellac. After applying generously with a brush or rag, allow to dry overnight. The areas that will blotch turn a bright yellow. This dissipates with time of drying, but it does turn a brilliant yellow. The next step is to sand all this stuff you want to be so proud of....
We can stop right here if you like. Sanding all this molding is gonna suck. To do it right and not cut corners is gonna suck even more.
Buy packs of a few grits. Buy something like Norton or 3M sanding sheets in packs of 5. get #100, #150, # 180. Some may aspire to #220, but not me.
Just start sanding. Use your hands and fingers to help curve the paper around curves and roundovers. It ain't rocket science but it all must be sanded. Before moving on to the next grit, dust off the previous dust. You are asking youself right now if they make a machine for this. Probably, but it ain't in the budget...keep sanding.
When you are ready to start coloring your beautiful molding, I have found the next method to be best for quick and efficient application of stain. This takes two people and is best performed on the lawn.
Get one of the large plastic buckets you bought and pour some of the stain you chose in the bucket. Make sure your molding is free of dust and dirt. Any last imperfections you see now will only magnify with stain and topcoat. Take care of them before proceeding. No time to cut corners.
Wet, stain laden molding needs to be placed somewhere, in the shade. You need to start thinking about wiping it off in about 10 minutes. With a pair of latex gloves under a car wash mit on each hand, have your associate start feeding you the molding. It gets fed over the bucket with stain soaked mits and should be fairly wet when done. Try to get the entire molding stained in one pass. After due time, do the same thing with clean, 100% cotton rags to remove the stain before it starts ro get a little gummy. Have plenty of rags and keep turning them to expose fresh surfaces.
Don't think that spontaneous combustion can't happen to you. Before disposing of oil-based, stain soaked rags, let them dry by laying out flat on a floor or draping over a surface. Balled up rags left that way can self-ignite.
You may want to make a few passes with this step. I always refer to it as "wiping it dry". Stain needs to be completely dry before applying a topcoat. After a few hours, small wet and shiny spots may appear. Rub thses areas again. In fact, rub all of it down while your at it, cause...let's face it; you've worked this hard...it should be done right.
Let the stain dry a good 24 hours, checking ocassionally for the wet spots. Are we havin' fun yet?
As far as the thick as snot stuff...chances are it was varnish, applied with a good brush, by someone who knew exactly what they were doing. Today, we call it polyurethane and it can be applied several different ways, with, I think the brush being your best choice. Keep it mind, skilfull brush work is a talent earned.
I think you would be better served to reduce the viscosity of the oil-based, Minwax Polyurethane by diluting it with 10% naptha. Naptha (lighter fluid) drys faster than mineral spirits (paint thinner). Get another platic bucket and use that. Do this is the shade on a cool day, or inside with the a.c going. If the stuff dries to fast, it creates problems. You want to be able to re-work your brsush strokes for about 2 minutes. You have to work fairly fast and you have to be neat. Any runs or sags you have now, only become something you have to deal with later. Pay attention now and save the aggravation. Once you have applied your mix to clean, dust free molding, you can go and relax. No matter what the directions say, it needs to dry for a day. 5 days is better. You always have next weekend for more molding work, right?
Uh...the bad news. Yup, it has to be scuffed with #220 grit or a Fine 3M scuff pad and another coat of polyurethane applied. Just like sanding, get to all the crooks and crannies with the scuffing. Your goal here is to knock down any rough or raised surfaces. The more blemish-free the first coat is, the better the second one both adheres to and flows on the surface. The goal here is 2 coats and maybe a little touch-up after installation.
Before I forget...you did buy high-gloss poly...yes? 2-3 good ($12.00) natural bristle brushes...a 1" and two 2" sash brushes. Paint thinner to clean the brushes and stuff? Buy a gallon. Take good care of your brushes.
Okay, after all this, your molding should look wonderful and something you can be proud of as a job well done...or, just okay because it turned out to be too much work.
Never lick a steak knife.