I've regretably never played a Freespace game, despite my love for the space flight sim genre, and I'm very very interested in getting this. However, for the time being, the only computer I have to run this game is my laptop with 2 GB of ram and an integrated intel graphics card. It's not really a 3D accelerator, but it did let me play Star Wars: Empire at War and the old-school Half-Life games, but not stuff that requires an actual card, like Painkiller.
So, does anyone think I can run either Freespace game?

I've played the first FreeSpace on PC with Pentium MMX 233 MHz / 64 MB SDRAM / S3 Trio 64V2 & Voodoo 2 16 MB -combination.
The official system requirements for FreeSpace 2 are 200 MHz CPU, 32 MB RAM, 8X CD-ROM drive, DirectX 6.0, 400 MB available hard disk space, Windows 95, 3D accelerated graphics card.
So... That means that you should be able to run it with full settings without any kinda problems. 'Tho if you're planning on testing unofficial FS2 SCP -"mod", that adds better graphics and more options, you'd need a bit better hardware. SCP needs "GeForce 5xxx or Radeon 9xxx or other OpenGL-compatible video card."
Just buy it and enjoy it. I know I will...

I originall played this on a DFI K6-2 motherboard, an overclocked AMD 500mhz CPU, an TNT2 32mb graphics card and 256MB of PC100 RAM, and Win 95B. Back then that was really high for a desktop.
Then Quake Arena and Unreal Tournament came out and I was feeling the pain.

I play Freespace 2 on a Netbook and it works fine. Since my Netbook only has 1 Gb of Ram, you should be fine with your laptop.

Both FS1 and FS2 were coded back in the days. Performance depends a lot more on the CPU than on the GPU.