Your question is a bit incomplete. I hope you mean insurance not assurance? There is no such thing here as paying a monthly fee to be sure that your car is maintained and/or fixed for a certain price also including your insurance. At least I haven't heard. I think you are referring to just insurance.
Fast answer for MTPL (or traffic) insurance:
There is a place now for querying prices on LKF (directly - car insurance foundation) website https://www.lkf.ee/et/kalkulaator. Is not in English but use google chrome translator if you need. You can query several car current MTPL prices there. Basically only "I am not a robot" check is needed and of your car's license plate.
To give you a better answer you are not describing your needs for a car. What period for? Which you are going to have a new or a old one? Then will you lease it or not? Where do want to use it - perhaps there are alternatives for owning a car here. I'll try to keep this one as close to insurance as possible but give some hints for others when considering having a car here in Estonia.
Insurance here is not that straightforward. They change prices quite often since market is small and market behavior can influence price fast. That means not everybody can keep up with the changes on their website. Also if you are a foreigner there might be some conditions that make MTPL more costly (risk of not knowing Estonia that much). Also how powerful car is, history of the car. You being over 30 means you are out of the most dangerous age cap and this makes it cheaper. Your history of insurance influences your price. Conditions like in any country. Price here is much more expensive if you use it in our capital Tallinn - outside of it price can drop a fair bit.
Insurance companies vs insurance brokers. Insurance companies sell the product you need. There are not that many on the market (LKF shows you them). Insurance brokers broke insurance companies policies. There are a bunch of brokers and I am not going to list them up here. Most known to me is Iizi: https://www.iizi.ee/en. But I buy my MTPL straight from a insurance company.
Casco vs MTPL. If you are buying a new(er) car and leasing it - then casco insurance is forced for you. There is no single insurance policy for a leased car combining casco and MTPL. Again casco has many criteria which will make the price. Also to get casco price you need to go to various insurance companies and brokers websites to get your price.
Why don't you consider renting? Longer period of renting can give you good prices. Also if you don't need to use a car often it would be better to rent one. Found a car starting from 10€/day on https://autolevi.com/ and there are more sites which rent cars.