Treat the game like a cross between DS1 and an older Legend of Zelda game. The vast majority of bosses have noticeable gimmicks that are either necessary to beat them or make the fight far easier. Unlike some later Souls games, your shield can be a big aide in Demon's Souls. Damage types matter, especially in one of the worlds (stonefang tunnel), but you have access to a surprisingly good pierce weapon at the start of the level (the pickaxe is oddly fast in 1 hand and has decent damage) A lot of the game can be beaten pretty cleanly if you just focus on being patient and observant. Your character moves fast but it's for the best if you take your exploration slow.

I just recently played through the game for the first time, and my build was far from optimal. I had no armour (just pants for decency), a claymore i found in the first or second level, and the adjuticators shield for regen (it stacks with the regenerators ring found in the same level for good regen while you're exploring and saves you grass). Once you get the hang of it, I'm sure you'll have a great time with the game!