To qualify for the 1031 exchange, do I have to buy a new property that is worth more than the one I sold, or at any value?

Any value, since "boot" can be recognized for cash-out and basis can be adjusted for adding cash in. 

A 1031 Exchange must be facilitated as part of the sale transaction, a person can't elect it after the fact. 

Thank you very much!

John

generally yes, though exchange expenses come into play. Less and part will be taxable. get professional help because there are many rules. Every one of them must be complied with. Non-compliance with any of them results in complete taxation while your money Is tied up in the new property. 

Yes, I read about the link that Chris shared: https://www.investopedia.com/financial-edge/0110/10-things-to-know-about-1031-exchanges.aspx. 

I think it is better to buy a property with a higher value to avoid an immediate tax. 

Another question: For example, my previous property was sold for $300,000 and has no mortgage, but the new property is worth $350,000. If I put down $100,000 and finance the remainder, will the $200,000 from the previous house be taxable? Thanks!