Hi...
The spec adamg67 listed would be par... any laptop meeting that would do you.
You'll basically become a fan of whatever DAW you first start using and if you pick up an, even cheap and cheerful, interface... it'll more than likely come packaged with a licence for one of the 'LE' versions of either Cubase or Ableton... they're more than enough for simple recording and editing of most tracks.
Now... I'll be honest, I use Cubase on an iMac and occasionally use a MacBook Pro if I travel somewhere and my spec are way in excess of what I need... I run a ridiculous number of tracks though and even that can become 'plugin heavy' so a couple of tips you might bear in mind that will reduce the burden on any machine:
1. For monitoring back as you play etc... use the interface control panel to adjust the buffer size depending on if you are editing or recording (higher for editing than for recording).
2. Work from an external drive... that is... record and store onto a different drive than the drive your software is running from
3. If you get into using a lot of tracks, and I suspect you might once you have the home recording bug, learn a bit about using group and effects Busses.
4. Consider some (budget dependent) augmentations to your recording setup. I am more and more using the Zoom H6 to record things like a double bass, which it can easily handle simultaneous DI and Mic. It also fucntions as an audio interface quite nicely and comes bundled with, if I recall, Cubase LE and Wavelab LE licenses.
Enjoy