It's been ages sine I played, but from what I mainly remember would be this advice:
1) Just take things slowly at first. You have an infinite amount of time to complete your goal, so just work towards the smaller goals (i.e. upgrading your house, getting married, etc.) instead of the main goal at first. I typically spend the beginning of a HM game with only 1-2 packets of crops planted, whereupon the daily routine was wake up, water/harvest plants, and explore the land until I had enough to expand my crops or get some livestock.
2) Figure out who you want to marry ahead of time, so you can dote on them early on. (Don't marry Jamie if you want to keep playing however. That's an immediate game ender.)
3) Spend time talking with the villagers & giving them gifts (Herbs and Berries at first until your farm grows big enough to give out produce). Making the other villagers happy will cause more to move in and events to trigger.
I want ToT. I ended up getting the Wii version, only because the GCN version was never released in Europe. Any tips on how I should get started? It's been so long since I actually played a HM, as soon as I started, I felt so overwhelmed. I've been playing in the little mine up from the central farm area and I can't find anything decent to ship.
Oh right, well that's changed my decision. I best look for the GCN version then. I'm just getting back into playing the Wii, and my first series of games to look for are the HM games. Have you played any of the other Wii HM's?