Transfer the minimum amount from the old computer
Transfer documents, music, pictures and video. Those are safe. Do not copy any applications or utilities, because, as mentioned in other posts, they will be old at best and will cause trouble, and will not work at worst because they will not run on an Intel Mac. Install current versions from installation CDs or DVDs, or from disc images ending in ".dmg" downloaded from the author's site. At first, avoid installing more stuff than you need, to let things settle down.
But first, if you bought your new Mac a few months ago, it will have the Operating System called "Lion" - OS 10.7 The current one is "Mountain Lion" - OS 10.8 To save you the trouble of setting up Lion then, later, installing Mountain Lion and going through the work again, I suggest that you install Mountain Lion now. You can get it from the Apple Store for about $13. It is in the form of a download which is several GB in size and will take some time, so do it overnight if you have a daytime cap on downloads. However, the download consists of an installation utility which is saved to your applications folder. That utility is overwritten once Mountain Lion is installed - don't ask why!. Therefore, do not answer "yes" to "Install Mountain Lion" (or whatever the invitation is worded), but search in your applications folder for a recently saved file, (list them in the folder by date, I can't remember the name). Right click it and choose "Show Package Contents". Navigate your way to "Shared Support" and find "InstallESD.dmg". Copy it to another folder. Doing this allows you to re-install Mountain Lion later, if necessary, without downloading the installer again. Then run "InstallESD.dmg" and Mountain Lion will be installed over Lion.
When you first run the new Mac it will ask you to set up your User Account. You should to do that, manually rather than copying across from the old machine. When setting up your email accounts, do not use anything from the old computer. You should start afresh and set them up manually. This minimises copying corruption or stuff that upsets the new Mac or operating system.
All this is quite daunting. Go slowly and patiently. Step-by-step, run things, install something else, run things...
Please let us know how you get on.
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