My Czech husband and I go back to his home every year to visit relatives, so I can say we have quite a bit of experience in renting cars there.
Book online and get all the insurance offered. Car theft is a huge problem & accidents occur more often with unfamiliar territory. Get the smallest car that would cover your needs with unlimited mileage at the cheapest company's pricing. Request an automatic transmission. We usually use a credit card to put the deposit for the car on(which will be voided out upon the car return) & my credit union ATM for the actual car rental cost(no foreign conversion fee). We have used just about every rental car company over the years. I can say it doesn't matter whether its a company like Hertz, Budget, Alimex, CS Rent a Car, etc - they all can be prone to problems of gotcha's. My advice is to go over the car with the agent inside & out like you are actually buying the car to have them note on the paperwork any scratches, dings, missing parts, gas gadge reading, etc at time of pickup and drop off. If there is anything unacceptable with the car at pickup, then have them give you another car. Make sure you have your reservation print out with you at pickup. Take a quick look at the owner's manual of the car before driving away if you have never used that make & model of car before. It is always nice to know how everything works before you get on the freeway. Keep your gas receipt from your prereturn petrol fill up.
Here are two cheap but good agencies we use.
CS Rent a Car (Czechocar)