Good tires is the single most significant improvement you can make. An AT or AT/MT hybrid will change it's off road abilities by leaps and bounds. Those more familiar might be able to suggest if you can go with a taller size or not without any modifications, I know many vehicles have a bit of wiggle room but I'm not familiar with that generation.
If it has anything like running boards or mud flaps, you might want to remove those so they don't go crunch over uneven surfaces. Running boards are notorious for hanging up on things and causing rocker panel damage over obstacles you probably would have cleared just fine without them.
I'd look into the transmission more, it might just need fresh fluid or something, but it needs a strong reliable transmission if you intend to try off road driving with it. No reason the one it has won't be, but if it's having issues now figure out why and if it's a real issue or just lack of maintenance.
Overall I'd say yes, that is a good little exploring vehicle. With some tasteful modifications it can be a quite capable little truck. I think they were a competitor to the 3rd Generation 4runner and are similar in many ways. Don't get too hung up on what you need to do to it, in the case of novices, the vehicle is usually much more capable than it's driver in the beginning.
Just use caution, don't go places you shouldn't, don't go alone if you think there is a good chance you might get stuck. Riding with sensible friends is the best way to gain experience without having to worry about what all you don't have yet, you'll learn what you need as you go. Don't throw money at it to equip it until you really know what you are buying and why.