So I'm very late to the party, but I've been playing this recently. Havent been invaded at all sadly (was playing in bodyform a while before i knew dying in that form hurts world tendencies) but I do see a lot of ghost, bloodstains, messages (some useful, some very funny!).
In tower of latria there was this sign that was set right before an item and said "real demon souls starts here". So i pick the item up (fluted set) and get "OVERBURDENED!!!!".

Luckely i could fat roll (with herculian ring) my way back to the nexus.
I started as a templar knight and bought the claymore which is now at quality +4. I also got the estoc up to +3 (regular upgrade) as secondary equipped. Got it up to this level very fast to be honest so the upgrade of weaponry doesnt seem as "slow"/staggered as say ds1/3. Ive only leveled str/dex (26/22) and vit (21) atm, and I killed yurt (i knew about this guy) so wearing his chest armor/leggings, with wizard guantlets and assassin mask.
I've done worlds 1-1, 1-2, 2-1, 2-2, 2-3 and 3-1. Now I'm trying to figure out where to go in 3-2 (no tips/hints needed though) which is fun - ive basicly lowered the fat blob by killing the fire praising hollows. The bosses havent been too hard, although tower knight took a few deaths with the starting halberd (not upgraded). It wasnt until i went back and bought the claymore that i much easily could hit his damn feet

1-1 and 2-1 boss were first tries. Flame lurker i got on second try. Dragon boss (i also got the dragon bone crusher!) took like 10-20 deaths, i stopped counting haha. 3-1 was the original pinwheel i guess (i had already spoiled myself about killing the guy upstairs from years ago so i knew i had to do that).
What can I say - getting to play a souls game for the first time is always great, and demon souls is no exception.
As a small sidenote: I've been playing ds1,2 and 3 all using keyboard and mouse only. Being 'forced' to a controller was a tad hard to get used to (I'm still not) and makes the game much harder.