Traveling around the world can be quite dangerous, especially since there is no ingame map and is easy to get lost. I suggest you start exploring bit by bit and slowly advance more and more into the wild, while learning to navigate by landmarks. When traveling also stay away from roads and well known spots, like mount spawns, resource spots etc… The less chance you have to meet a player the safer you are. Always try to stay in grass, forest or mountains and try to find alternative (altho longer) way to your destination, it's usually safer that way. You can see monsters and predict their movement, if you don't get too close they won't attack, and even if they do, you can outrun most of them. Keep in mind also, mounts run uphill slower, use this to your advantage if chased by someone on mount. Save your stamina for sprint when you need it and learn to dodge.
And by all means, don’t announce to the world where you’re going and what you’re carrying, you’ll get ambushed fast that way. When traveling far I suggest you always head into nearby town first, to bank items and station yourself there and go to your hunt/gather spot from there.

Some of town layouts to help you find certain vendors (all credits to original authors, this is just a collection of images I found on the internet).

Tindrem - The biggest city in MO and a great place to start. You can find mostly everything there from books, crafting stations, nice starter area with many resources and couple of nice farm spots just outside of it’s walls. The downside is it has a lot of people in it at all times, which makes it difficult to avoid players that will want to harm you. I think if you keep your eye open and stay away from graveyard it’s still the best place to be and earn some starting money.

Morin Khur - Second starting place for new players surrounded with mountains. A little less riches around but still enough to get you started. Graveyard is a bit more remote with a few interesting spots (like a cave full of undeads), which is a plus since players are more spread out, but also is farther from town and guards if anything goes wrong. The downside, and also the reason I prefer Tindrem as starting point, is the fact that you need to travel quite far outside of town through a valley to find anything worth hunting, which can be quite dangerous and is many times camped by red players.

Toxai - A town just pass the Morin Khur graveyard beyond cliffs. Nothing much of interest there for new players, except for maybe Animist Librarian.

Meduli - South of Tindrem by the sea is a desert city of Meduli. It’s a nice place because it has many resources, especially for miners. It’s open nature does attract some amount of red players, so be careful if you go there.

Fabernum - Another town in the mountains, NE of Tindrem. Plenty of resources, nice town layout, but proximity of Kranesh makes it that you’ll have a high chance meeting a red player.

Vadda - Small city in the woods with plenty of trees and forest animals around. Most of the time it’s safe there and there is Zoology librarian near the town.

Bakti - A city in the south above the jungle. If you go to jungle this will most likely be your outpost. Some amount of PvP going on around, so it’s good to be careful.

Moh Ki - Seems like a quiet city, haven’t been much there but it might be a good place with little red player activity.

Kranesh - As a new player never go there. It’s a lawless town full of red players.

Gaul Kor - A remote town far in the mountains. Never been there, but since it’s lawless I guess it’s better to stay away from it as newer player.

Cave and Jungle Camp - Two camps that are lawless. They mostly serve as outposts when you’re hunting in the area.

Sarducaa

Sarducaa is a very good place to go to make money even as a new player. Simply going around and gathering flora will earn around 5g in 10 minutes depending on where you go. However to rich players this is not necessary. However heat damage puts most people off. Scale armour is the best heat mitigation armour and isn't that expensive. The jungle in the north is also a place of interest. Things like scorpions and Nahuat can be found.

Beth Jedda

The capital of Sarducaa, where most players are. Unlike the rest of Sarducaa in Beth you won't take heat damage. Most breeders come here to sell desert horses. Beth is the closest city to the bridge, so going to Sarducaa go there first.

Belrim

Located on the west coast of Sardicaa, Belrim is another major trade post, used by many different guilds. Another good place to go if you have things to sell.

Pash

Another town in the southernmost part of Sarducaa. Pash is very dangerous due to the red guild owners. Not a useful place to go to.

Aur 

Aur is a small town in the northern jungle. It mostly serves as a temporary drop off point for goods attained in the  jungle.