Hello, received a bike from a friend a few months ago. It's a trek mountain bike (don't know the model) and I got to ride it for two minutes before both tires popped. They were already written down and I'm sure the ghost heads and tumbleweed didn't help.
I've been looking for new tires but I really don't know what to get. I need tires that can survive goatheads, tumbleweed, unpaved roads, roads so poorly maintained they're practically gravel, and a normal paved road. I'm going to use the bike to commute from my house to my new job. I can't drive and I don't plan to drive for awhile.
The numbers on the side of the tire were worm out but I think I made out that the tire size was 26"x 1.05"(or 1.95")

I also heard that there were solid inner tubes. I tried looking it up but instead got articles on how to install them not where to get them.

Sorry that this post is poorly structured, I kinda just woke up and my first thought was "there's probably a bike forum that can help you." So I've been awake for tops 7 minutes. I can clarify (hopefully) if you have any questions.

Solid tires are awful. There is no technology that is as efficient or comfortable as pneumatic tires. Solid tires have very little compliance, so the result is an extremely harsh ride which will cause more expensive failures elsewhere on the bike.

if you live where there are goat heads, tubeless is likely what you need, but you probably do not have compatible rims.

you could try putting tubeless sealant in your existing tubes.

You don't ned anything really out of the ordinary. The tubes/tires just both need to be in good condition (not old, dried out, worn thin, flattened, pinched, etc) and work with each other and the bike. So anything you get to freshen this up will work for a lot longer then those old ones did just by virtue of being new!

26 x 1.95 will be a really easy thing to replace - your bike likely has capacity to go a bit narrower or wider than that, so don't worry if you end up with say, 1.75 or 2.15 or something, as long as both the tires and tubes are 26" / ISO 559mm diameter.
For tires, you want something that has some tread knobbiness to dig into your mixed surfaces, but that is not too massive and rubbery so as to be heavy and slow on-road. Something like this I'd say: https://www.biketiresdirect.com/prod...?fltr=3750+225
As for puncture resistance/tube choice, they do make some with a layer of sealant so if you get a small puncture the "slime" stuff can help to prevent the loss of pressure. Again, just. make sure right size and valve stem type (likely Schrader) - https://www.biketiresdirect.com/sear...brnd=&fcat=cmu

There are tire liners for mtn bikes by Mr. Tuffy which supposedly help prevent flats which go between the tube and the tire casing. Can’t say how effective they are, but when combined with the Slime solution above may help. Keep your tires well inflated to reduce pinch flats.

I have been running Mr. Tuffy's on my three bikes since 2009 out here in Colorado where the goat heads roam. Before tire liners, 1 to 2 flats a month on my street tires due to goat heads. Since Mr. Tuffy's tire liners, 1 to 2 flats a year, and not due to goat heads (or glass...usually nails or heavy staples through the sidewall).

And with tire liners I can run thinner, more supple (and cheaper) tires. My MTB-based commuter has WTB Slick 26x1.85 and they have made the bike fast and fun!

I had tried heavier, more puncture resistant tires on my newer road-bike based commuter and they also resisted fun. They felt heavy and slow.

There isn't a lot of love for tire liners on bike forums, but I recommend them.

Can’t help you with goatheads and tumbleweeds.
Unpaved roads generally isn’t much of a problem.
It helps to learn to recognize what caused the flat.
Penetration flats need another approach than pinch flats.
Bicycle tires are very different from car tires WRT pressure retention. Even on MTB widths, topping up weekly maybe sensible/required.
Get a floor pump with a pressure gauge together with your new tires.
Despite that, hitting a bad pothole/curb/rock can still give you a pinch flat.
Knowing how to ”go light” - get off the saddle, knees and elbows bent, let the bike move beneath you - when you pass a bump is a worthwhile skill to learn.
Sitting like a deadweight will be harsh on both bike and butt.
I’ve been quite pleased with Conti Sport Contacts, but they might not be rugged enough for your use.
There are plenty of tires out there with different kinds of (penetration) puncture protection. There are tire liners(Mr Tuffy) that can be used. They’ll all cost you some in rolling resistance.
I’ve used solid tires and didn’t think they were entirely horrible. But I have mostly decent roads.
I haven’t tried the solid inserts due to the way rims and tires work. Tires need part of the bead to be able to slip into the deepest part of the rim to get the last of the bead over the edge.
With inflatable tubes, this is generally not a big deal. With solid inserts, it can be a considerable challenge. I’ve seen some videos. Really squishy ones may not be so bad to mount, but will have high rolling resistance.
Tubeless have considerable recovery ability WRT penetration flats, but setting up, particularly if rims aren’t intended for it, can take some time.