Specs - As a general rule, you're always going to get less for your money with a laptop. $1000 would get you a pretty good laptop; or it would get you an awesome desktop.
But you're probably going to have to upgrade either way. If you're running Windows '95, you will most likely need to upgrade to Windows '98, at least. And 64MB of RAM is really stretching it - a 256MB stick of PC133 SDRAM will cost you $35. Thats an easy upgrade that should bring a speed boost.
Now if I'm remembering correctly, the Celeron 300 came in two versions - with and without L2 cache. If you have the one without L2 cache, I really doubt that it's going to be fast enough for any recording applications. If it has L2 cache, it's highly overclockable, and you might be able to get it to run at over 450mhz - but then, new CPUs are so cheap, it almost isn't worth the effort and risk. And if you did that, you'd have to upgrade the RAM, because you're most likely using PC66...
Finally, the hard drive. It's probably 4500RPM. I would think about upgrading, even just to a 5400RPM drive - when I first got into recording, I had a slow dinky 3GB drive. It worked okay. I could only work with about 6-8 tracks at a time, though. Somewhere along the line, an acquaintance gave me his 5400RPM 8GB hard drive. I figured anything would be an improvement over what I had, but I was surprised at just how much of an improvement it was - the new drive was over twice as fast as the old one, in benchmarks.
I would say that you should try some audio stuff with your computer before making a decision. If all you want to do is master with it, you might just need some extra RAM, and that's it; but if you decide against buying a laptop and want to use your desktop for recording, you may want to consider putting together a new desktop or upgrading the one you have.