which type of record is best to use in appian?

All three are really different. 

1. Entity-backed record - It is used when you operate on a table. When your source of data replies only to one table. 
2. Service Backed - When your data source doesn't sit on Appian but rather comes over via Integrations. 
3. Process Backed - When you want to report over the various variations of data that have been sitting in the process instances of the processes. 

There is no best or worst. It all depends on the use-case. But most of the times, you will find yourself using the entity backed record. 

All three are really different. 

1. Entity-backed record - It is used when you operate on a table. When your source of data replies only to one table. 
2. Service Backed - When your data source doesn't sit on Appian but rather comes over via Integrations. 
3. Process Backed - When you want to report over the various variations of data that have been sitting in the process instances of the processes. 

There is no best or worst. It all depends on the use-case. But most of the times, you will find yourself using the entity backed record. 

thanks for answering ,but is there any different among this 3 based on performance.

I think there shouldn't be any performance difference as long as you are using Record Sync

Your choice should have nothing to do with performance, but where the data comes from.  Does it come from a table, or a webservice you call, or from a process or group of processes Appian is running?