You can explore if you want BUT when you first start out in the game even a lowly bandit is too much for you to handle. No shame in running away in this game. You can proceed at your own pace. Best bet is to put at least one of anything you find into storage. NEVER give away your only copy of anything. There's a place in Gran Soren called the black cat where you can get duplicates made. You don't have to rush through the game, doing the side quests is fine.

It's like this.
The game has a few "stages", where the world changes in some way and more quests and places are available to you. Once you start the game, there's only a starting village, and you can't go very far until you do a few quests. This is a spoiler, but anyway - once you do a few quests, you'll reach the capital of the kingdom. This is I think, "stage 2" of the game. It'll open up considerably, and you now can go everywhere on the main map. There's nothing stopping you from venturing into the far lands, except strong enemies. There's no time limit or anything.

HOWEVER, even if you can go anywhere on the main map, a few locations will stay closed until you actually progress enough in the story. Some locations are just barred by guards, but in others, you can actually go inside and almost fully explore the location, but there'll be a portion of the place that will be closed off because you don't have the necessary key. This key will be given to you during a story quest.

Now a tip about quests. Just because a quest is available, doesn't mean you can do it. There are three types of quests:
- story quest
- npc quest
- notice board quest

Story quest is self-explanatory.
NPC quest is a quest where you need to talk to an NPC to start it, they usually have a small plot.
Notice board quest is kind of like an MMO quest, where you need to "kill x enemies" or "gather x things". Now this here is where you can't just go off the rails. There are a few quests marked as "Escort:". This is a quest to escort an NPC to a faraway place, and very usually you will never be in any way ready to do this. You'll have to protect an NPC through a lot of enemies, and nowhere does the game have a "recommended level" stat. So just don't start those quests until you're WAY into the game. Like, 30 hours into the game.

You can take your REAL time for the side-quests, But they all should be done before you do any of the main-quests. They're not realy marked, but you can consider all the quests, that have something to do with the duke as main quests.

EXPLORING is important.
If you don't do that, you might miss the one or other (none-blackboard)-side-qust and may be locked out of certain areas...

All this isn't the case in DD 2. So, if that is realy your intention, part 2 might be a bit better for you.

That said, both games are realy good and have specialities, that no other game hase.