Logrotate is a good tool for log rotation and compression. It is available for most Unix flavors. I find the defaults used on Ubuntu to be a good starting point. When changing rotation frequency, you should change the rotate count.
Keep logs as long as they may be useful. Archive to non-disk storage if necessary. For business systems there may be legal requirements directing retention and/or destruction of log data.
Depending on the data and availability of data in another log data may be kept for a week, a month, a quarter, or a year. Only duplicated data is deleted after a week. A monthly backup retained for a year will give you a years worth of most log data.
A centralized log server generally serves a different function than log retention. Comparing the centralized logs to host logs may detect log file tampering.