Since you have a computer, is there some reason you want to keep a paper log? There are lots of free amateur radio logging programs. Personally, I use the logging program that comes with DM780. This is actually a whole suite of useful amateur radio programs and the log book is just one of them. The primary use for DM780 is for working the digital modes such as PSK31, RTTY, etc.
If you just want to keep a simple log on paper, you can just create a spreadsheet. You need a column for the date, time, frequency, the other person's callsign and name, and a space for any notes you want to make about the contact.
As far as the time, amateur radio operators use UTC time, sometimes referred to as Zulu time. This is very important when making contacts with people in other time zones, but since you will only be making local contacts, your local time might be sufficient. Personally, however, I think you should start getting used to logging contacts in the UTC time format. If you decide to upgrade and work HF, this will become absolutely critical.
As far as frequency, you might also want to make a column where you can put either an "S" or and "R" to indicate if it was a simplex (or direct contact) or through a repeater. There is a lot of other information you can keep, but that is totally up to you.
I gotta tell you however...
That most amateur radio operators generally do not keep a log of their local contacts. For most people, they use the VHF/UHF frequencies to chat back and forth with friends and a log book would fill up really fast. While there is nothing wrong with doing this, my guess is that you will get tired of logging every single contact you make through a repeater.
My advice is worth exactly what it cost you - $0.00. I have been involved in amateur radio for nearly 20 years and most of my opinions are based on my experience over those two decades.