For starters, the world map of MonBre has numbered the cities in the order you're "supposed" to visit them, so that should give some clairvoyance. The note icon in City will show you also where you "should" go next. There are quests out there with really amazing rewards, and people with stories to tell. Some quests are chained and don't show their best reward until you get to the last part.
The following tips are tips that I, Vael, creator of Monster Breeder, feel would applicable to success in the game.
• Raise different types of monsters for exploring. A quick one that does mediocrely-hard hits and has lots of HP will be great. Other types are a strong and accurate hitter along with speedy, or a good chump-blocker monster. MonBre is designed to not have many "bad" choices for play styles.
• You may want to consider raising two exploring-monsters at once. They'll help you a lot during boss/god battles and will make great splicing partners.
• It's a good idea to get as many monsters as you can. MonBre's not a game that you're going to be beating in a week. This is a game that rewards long-term planning. A typical setup I suggest is to have 3 worker monsters constantly making you money (and splice partners!) and 2 combat types.
• About zealous attack types - watch out. Strong and fast with complete disregard to defense might not always be the greatest tactic. Of course completely using a chumpblock monster, as I've said in the "Stats" section, does have protections in place, so don't even try it. ;)
• Breeder level, don't just shrug it off. Those few SRP you get in the longrun can really add up. Don't hesitate to buy a bigger house instead of getting a better equip. Equips can always be found from killing a mob, and usually are better.