I've got the making it secure part covered. What would you do on the inside to keep moisture levels appropriate for storing guns? Is there a certain wood you would use to line the inside?

Is it climate controlled?

No, so wondering if a dehumidifier will work.

Look at these dehumidifier rods
https://www.shootingandsafety.com/best-gun-safe-dehumidifiers/#1_Lockdown_Dehumidifier_Rod

The room will probably be 8'x6' with an 8' ceiling.

In our climate you might consider spray foam. Just having a lower 24 hour temperature variation is a good start.

The shop will be insulated, but I was also thinking about insulating the room.

A couple 5 gal buckets with cat litter/absorbent material plus a dehumidifier...especially if you are east of I-35....

I have had my safe in my garage (detached, not insulated) for about 7 years in the Houston area so VERY high humidity. I keep 2 cans of silica and a large Golden Rod in it. Humidity stays about 45% in tbe summer and I haven't had any issues with rust or mildew.

Those do not reduce humidity. They only warm the air and cause convection to keep moisture from collecting on the guns in a small space like a safe.

One of these will give you peace of mind. Can be set to desired humidity level and drained by hose attachment to drain, sink or outside.

Insulation will help tremendously as mentioned above.

These work. There’s one in operation in the lab I’m sitting in right now at work.

How often will you access the room? Some of these require maintenance.

I would think around once a week. It will be guns and ammo.

Dehumidifier should do it then.

I’ve had my safe in this house for 3 years and use no humidifier or anything and they have showed no rust or anything.

Yep, but yours is in your house.

My thoughts in no particular order.

Water will alway migrate to the coolest location. Cooling to room could increase the humidity durring low load damp weather. The ac would not run enough to remove the humidity that migrates into store room.

A mechanical dehumidifier is basicaly a window ac not vented to the outside. The evaporator is placed in front of the condenser. The electrical power consumed will raise be result in heat gain in room at the rate of 3.4 BTUs per watt. Mechanical dehumidifiers will generally will not work below below 40 degrees.

I would expect a mechanical dehumidifier would be good option. But you need to watch temperature rise in summer.
In winter, you may have add heat. You would only need to keep the room a few degrees warmer than shop. But if you heat the shop with out adding heat to room, water could migrate to room.

In cold weather heat will drive water to cooler location. In summer mechanical dehumidifier would do the work.

Insulating room could be a good option.

In commercial applications, operating expense is usually not a consideration. We use climate control and reheat the supply air supply.

6x8 is a small area. Not going to take much.

Another thought

There are some bathroom thermoelectric dehumidifiers. I have no personal experience with the dehumidifier version of the technology. This the same technology used in 12 volt drink coolers for trucks and cars.

Edit...
Power consumption is 60 to 75 watts. This would result in very little heat gain in room, if room uninsulated.
I could not find a oprational temperature restrictions. But, they designed to be in climate controled ambient.

If I remember correctly, there is a 40 degree difference between plates. 80 degree ambient is desired. Rolm temp above or below may negatively impact performance.

But they are cheap, in the $50.00 range.

Sorry I typed that way too fast lol meant to say my safe has been in the garage at our new house for 3 years. It is attached but no climate control in it. No problem at all with guns in the safe or out on the work bench for long period of times.

IMO you are playing with fire - especially with any left exposed. My brother brought some of his rifles to me for storage in my insulated shop room. They were left on the pool table. We had a big temperature swing back in April and one of his old Winchester Model 12s was basically ruined and is now just a shooter. Some of the others had minor rust specks that thankfully came off easily. This happened in a span of 36 hours. It’s big temp swings that will cause the issues.

All the guns got a new coat of RemOil, the A/C was turned on for climate control, and the dehumidifier above was installed ASAP.

I emailed the one person I know that built a "safe room" in his shop. It was 12x18 underground room under the slab of his shop building. It has a vault door on a concrete closet inside of the safe room, that he keeps some valuables in along with what he calls his survival weapons. I asked about humidity, he said he has a humidifier in the basement area, and another in his valuables closet. He reported no rust problems. But he is farther west and they have low humidity, almost non existent.

A couple of 100 watt bulbs will keep that size dry

How will light bulbs keep anything dry?

Regular incandescent bulbs put off quite a bit of heat.