I would consider this too much for one rack. You always want to leave yourself at least some space for the future. I have seldom been in situations where less space is used in a rack over time, rather quite often the opposite (you end up needing more).
Figure it this way:
- Typical 48 port switch = 1U
- Typical 48 port patch panel = 2U
- Typical full rack = 42U
For 600 terminations, you will need about 39U worth of switches and patch panels, which doesn't leave much room, especially for things like UPSes or any other equipment.
If you decide you want any horizontal cable management, there isn't room unless integrated into the patch panels and then depending on brand/model, these may be 3U.
If you go with a chassis based switch solution (now or the future), this also wouldn't work as usually these are not as space efficient (while line cards take up only 1U, their power supplies will take up additional space).
If you need to add more cabling in the future, again you wouldn't have space.
Go for the second rack and give yourself some space.
Edit: Adding this to comment on some of the other answers. I left the actual rack layouts out of my answer originally as they are an issue for much discussion as there is no "correct" way to do it. While several good ideas are proposed, a rack design/layout has to address the concerns of your environment and what will provide your organization a reliable and manageable solution.
While there are some things that should be done for any proper installation (racks should be properly grounded, if you use two post racks a ladder rack or other means of securing/stabilizing the top should be installed, etc), many of them come down to personal preference.
For instance, some cabling companies will tell you that you should not put patch panels on the lower 1/3-1/2 of the rack, as it is harder to terminate and prone to more errors. Some will say you shouldn't do any sort of patch panel/switch/patch panel layout as getting access to the back of the patch panels (for additional cabling or repairs) can be restricted.
In earthquake prone areas, some people will tell you that you should mount your equipment in the bottom half of the rack (with heaviest items - UPSes - at the bottom) as this provides a more stable rack. The more weight at the top of the rack, the more the rack has a tendency to sway.
Ultimately, you should put thought into any rack design. Think through the tasks that you will be doing most often, the tasks that are prone to mistakes/errors or can affect other connections, the amount of space you have, your budget and any other considerations the job/site may have.