You must arrange insurance before you get the plates. You contact your insurance company of choice and tell them the information that they need to offer an insurance policy on the car. If you are going through with the purchase you tell the company that you are buying the car and they will send a letter of intent to insure to the SAN. They don't send anything to you at this time.
The garage shouldn't need to see proof of insurance unless they are going to take care of the paperwork for you and get the plates for your car.
You can't get number plates until you have a cancelled gray card. Which is the registration papers of the vehicle. Your previous owner must have cancelled their registration on the vehicle. This releases them from ownership and responsibility and liability for the vehicle. When the grey card is cancelled the insurance policy will be cancelled.
I.E. If you don't have a valid and current registration then you can't have insurance on the vehicle. If you don't have insurance then you can't get the vehicle registered and plated. It is kind of a catch 22. I found this to be the biggest PITA. How to get plates for you car when you can't drive it because you don't have insurance until there are plates on your car.
Your car doesn't have to have an MFK before you agree to buy it. But as with anything else there are some caveats.
Your car must have a valid MFK. This means that if you don't have one you will have to get one before you can get plates. It also means that if the MFK on your car is getting close to expiring then you will have to do it at some point after you own the car. My opinion on this, having done it myself, is that you should get the current owner or garage to do that MFK before you agree to buy the car. Others have said this as well and I would go with their advice. If there is nothing wrong the car then the MFK is trivial and inexpensive. If not, then meeting the requirements of the MFK will probably be very expensive and could be time consuming. After all you wouldn't have a license for the car nor insurance.
Another thing you need for your car is certification of meeting emissions requirements. This must be done every 2 years. Most people forget about this but if your sticker isn't up to date you can be fined for it. If it can't be easily done this is another thing that can become expensive.
Basically, if you can't get the current possessor of the vehicle to do the MFK and the Emissions test and get them both passed then I would run and not walk away from the situation. Don't listen to admonitions that the car has a valid MFK and Emissions Sticker. Have them both redone as a sort of proof that the car meets requirements at the time of purchase.
You should have the following when you go to register your car.
1. Cancelled grey card (registration) for the vehicle.
2. proof of MFK.
3. proof of Emissions Control.
4. Letter of intent to insure.
5. Letter of sale. Some document that says that the previous owner sold you the vehicle and you bought it and for what consideration. I.E. how much money.
6. Your Identity Papers. Makes life easier for the people at the SAN.
They will issue your plates on the spot, unless there is something wrong. You will receive a billag in the mail later by the end of the month.
Your insurance will go into effect immediately and you will receive papers to sign and return in the mail. I can't stress how important it is to sign and return these papers as soon as you get them. If you fail to do so and have an accident you may not be covered as you are not legally insured until you have sign and returned these papers. You will not receive a billag until you do so. If your policy is cancelled because of your failure to sign and return the papers your registration will be annulled. Eventually, the police will ask you to return your plates. If you fail to do so the police will eventually confiscate your plates. It goes without saying if you have an accident without being properly covered you may be SOL.
Don't forget the ask for the certification of any and all modifications made to the car. This includes roof racks, any non OEM wheels, etc. If you are pulled over and don't have certification of any modification that might affect the roadworthiness of the vehicle in any way you can be sited and possibly fined and/or have your registration revoked.
If you travel outside the EU then you should ask your insurance agent for a "Green Card" that is proof of insurance in other outside countries.
It is a bit of a wind-up but if you cross your t's and dot your i's it is actually quite simple to do by yourself. When in doubt, I have found that the people at the SAN are helpful and will tell you exactly what you need to accomplish your goal.
Good Luck,