Gold or RL money ?

In both cases : A LOT.
Unless you're willing to get broke ingame and in real life, be prepared to furnish your house over time (over a LOOOONG time) step by step, and not on day one.

By my (very rough) estimate, at least 10x the cost of the house itself, specially if you want to display trophies and the "fancy" versions of furniture.

Depends.

You'll need to find the right furnishing plan, of which there will be around ~2,000 according to ZOS. That being said, plans will probably be expensive the first week or so, especially for purple "high-tier" styles like Altmer or Breton. It will take a decent amount of farming raw mats to craft new furniture since there are also new materials you must harvest from nodes.

If you have a crapton of mats, you will probably have to pay around 20k per design after the first week. People will be farming like crazy so it will go down quite fast. I would suspect much higher for raw mats in bulk.

Also, some things won't be obtainable (I think) when I was on PTS, like trees and plants. Many trees cost 100-400 crowns per tree, so stock up on some crowns as well if you want some aesthetics.

My suggestion: stock up on style materials and processed materials while you still can. If you want to make some quick money post-Homestead, save up your yellow resins as well.

There are plants and trees at vendors in each zone's main city, or just outside it. Many of the things will have achievement requirements tied to their availability.

So the furniture is suppose to get the players more involved in crafting. Sry showing newbness again. How long does it take to level up crafts and which crafts will be most used for making furniture?

Housing should be a another Great profit for some. I can already see all the empty manors day 1 and the QQ threads on forums for furniture grind. Crown prices will be a laugh and a whole other topic.

When housing goes live our characters wont have any blueprints, we will not be able to craft a single item.
The housing blueprints drop like provisioning recipes and are random world drops in drawers, pots and rarely from killing enemies. Supposedly from pickpocketing and murder but on the test server one player murdered 100 citizens and didn't get a single drop. So far its been reported that the drop rate is low for blueprints.
It has also been reported that the special furniture materials required to craft also have a low drop rate.

Crafting your own furniture will take a long time looting pots and drawers hoping you get lucky. Even if you get blueprints they might not be the ones you want. It will be random and youll have no control over what you can craft.

At first I am guessing that due to how hard it is to get blueprints and materials the cost of furniture will be very expensive to buy from players/guilds with gold. I am sure after a couple weeks or months when more players get blueprints prices will go down but from what ive seen of the material requirements to craft I think it will always be expensive to purchase with gold. If you want to furnish right away be prepared to spend lots of gold or real cash.