I don´t know from which EU country you are, but I came to Finland 2 months ago, and except KELA registraction everything went fine.
At first - go back to the police. You can always try to apply for the RP again. OR go to Sweden for couple days, get a document about it from the local police station, and come back.
When filling the form for the RP/registration, write as the reason to moving to Finland as "an EU citizen". They gave me this advice at the police station.
Then hopefully you have a health insurance in your home country, they will want your EU insurance card too. Give them the copy of your bachelor diploma. And bring the original too, to show it to them..
Then write a "proof of sufficient founds", that you have enough money to take care of yourself. Noone will check your accounts, so you know what to do

The best is to have over 6000€. And you need to write how much are you going to spend/month. What are your expenses for rent, etc. So all the costs. Those try to keep low.
Hopefully I did not forget anything.
I have a master´s degree, I gave them my bachelor and master´s diploma too.
One more thing - it´s good to ask for the registration right after arriving to Finland.
For me it took exactly 2 weeks to get it.
I wish you a good luck!
And don´t give up!! Nothing is impossible...