Get some or request the KILZ brand primer, it will help with bug and mold/mildew issues in the future.
Bare wood should always be primed, despite what the paint brand says about no need for it. It will extend the life of the paint job by several years.

More grip than regular Kilz.

Bare wood is going to soak up a lot of paint, and the gallon you bought won't go as far without priming.
You can get five gallons of the Kilz2 for around 60-75 dollars. The leftover will come in handy for later projects. Just seal it up well and give it a shake or stir every now and then. I'm still using remnants from a mural project several years later.

a good source in my experience ... and they make great products durability and application wise. Go with their advice.

Have you treated the ground around the founation for termites?

Ask the termite guy if their primer has the stuff like Lunasea mentioned, if not, get 'em some and let them put it on and finish their gig. Then you and finish paint with the gallon you just bought.

"sat work?

for a job worth doing well, use a good primer...

Some paints are called 'self-priming', that actually contain no primer, and I don't see how they can be anywhere as effective as a separate primer coat. The primer will help the paint coat adhere, and, if you use Kilz or something similar it will help to control mold problems.

Depending on the color you are using for the finish coat(s), you can use a light (white) or dark (usually grey) primer so you don't have to apply as much of the topcoats.

Here's some good background info on the use of primers and what 'self-priming' paint is actually good for:

https://www.thespruce.com/self-priming-paint-real-or-scam-1822383

Zinsser (red can) is a good choice

There was dry rot but no termites.

What you need to do it get rid of the termites and dry rot first. You need to hire a contractor to do this and have it all removed and replaced with new wood before you can proceed. Check all windows as well and replace them if necessary. It will cost you, believe me.

After the dry rot/termites are done and gone, then the paint.

You need to hire a painting company to do a decent job.

First, they wash down the entire house with a pressure washer that will clean the debris, etc. off of the house.

Next, you need to have all of the nails set and then comes the primer. The entire house should be primed after the nails are set.

Now you can have the painting done. I would not recommend Sherwin-Williams and their product called "Super Paint". It supposedly removes the priming part of the job but does it work? I read the reviews of this paint and was unimpressed as they wanted to paint the house with this. I called the Sherwin-Williams store where I live and even they were hard pressed to recommend it.

The old painter I hired with his son has been in this business for many years. He used what he called "Peterson" paint on the house. His son hit the back of the house where the southern exposure gets hit hard with sun, he gave it 3 coats.

It took almost a week to do the job but they did a fine job. They put some of the paint samples I had picked out on a small patch on the back of the house. It did not look anything like the samples! I decided to change the colors to a more muted scheme.

It worked out really good and I hope you can find a place to do a good job. Don't skimp as it is not worth it.

The job I had done last year is good for 10-15 years if I live to see it!

Best of luck SHRED!

Agree with the suggestions of Kilz or Zinnser. An alcohol based primer is your best bet, however, it will stink and you will need to make sure you have adequate ventilation. The good news is that it dries quickly, and can be repainted in a short time. Hope this helps.