DNN itself has scheduled tasks to keep the log size down, but what often fails for people is the actual Sql Server log file. Each insert/update/delete is logged in Sql Server tranaction logs, so if you have a database corruption you can restore back to the point of failure. A lot of installations of Sql Server 2000/2005 have logging setting far in excess of what is needed for a simple website. You aren't storing complex financial transactions between banks, so you don't need the top level of logging.
Just set the Sql Server log type to 'simple' and when the daily backups run, get the truncate log on checkpoint to run. This will keep the Sql Server transaction logs down to a reasonable size. You can truncate the DNN log tables on a regular basis if you like, but there are scheduled tasks and settings within DNN to achieve this.
My suggestion for the 'long' startup time? Do some SEO and get yourself some traffic. Any site with a decent number of visitors isn't going to unload itself. What's your site for, anyway, if not to attract visitors??