Both.
No portastudio is self contained enough in my opinion. A PC is by far the best place to finish mixes and make CDs and mp3s. Although there are good interfaces for laptops, a portastudio is by definition better for portable multitracking with the mimumum setup - especially for a newbie.
For the pc, you still need a decent soundcard, but one with 2 analog in and out plus s/pdif in and out will suffice - like the new
E-mu 0404.
When selecting a portastudio, bear in mind how it can be connected to a pc or how you are meant to archive your tracks. Having to burn a CD from an internal or optional CD burner is not too bad and you can make roughs for people after the session easily, but a USB connection that lets a PC copy off the recordings directly is better.
As you're inclination takes you, you will have a choice of working practices.
1: Do all multitracking in the portastudio and treat the pc as a 2 track mastering recorder - you can store a hell of a lot of stereo mixes on a pc hard drive.
2: Use the portastudio to capture tracks and import them into a PC multitrack program like Sonar or Cubase and avail yourself of the wealth of plugin FX and mix automation this approach allows. A portastudio is pretty much fixed in what you can do, while a pc program can grow with you.
I mention all this because a frequent question in portastudio forums is "How do I get my mixes to CD or Mp3?". In other words, people have spent the time and money in getting the recordings, but not given a single thought to making the final product until they got to it!