First question: what are your laptop's specs? Is it PII, PIII, Celeron, Athlon, Duron? How much RAM do you have and how much can your system take? You can go to
http://www.kahlon.com or
http://www.crucial.com and type in your PC's model number to find out RAM type and maximum.
Second question: can your system support upgrading to a newer version of Windows (or possibly going back to Windows 98 if necessary), even if it's just going to Windows 2000? Okay, most modern trackers will support Windows 98/ME, but ME is terrible. I'm not laughing; I've had to deal with ME at work, so I can sympathize.
I've successfully run ModPlug (pre-Open ModPlug) on a PII 300MHz with 96 MB and Windows 98, getting something like 96 voice polyphony, 44.1kHz 16-bit stereo mixing, and cubic spline interpolation--but, that didn't involve any VSTs or DXi (or their effects counterparts...not sure what their exact title is). That was pure, sample-driven tracking.
However, to make use of a lot of the newer features in trackers, like DSP, synthesis, and routing, you're definitely going to need more machine than that to handle the load. My PII had serious trouble with playback in MadTracker 2.2, where the recommended processor is a PII 450 with 64 MB of RAM, and MadTracker 2.6 recommends a 1GHz with 256 MB.
That said, if you're just planning on taking sample-only tracking (or mostly samples) from a DOS environment into a Windows environment, ModPlug is probably the least demanding choice. If you've got a PIII or K7, you might be able to play around with some of the more exotic features in MadTracker, but you'll still be limited in how far you can push things (I'm basing this on specs a typical Windows ME machine might have, i.e. Athlon 750 MHz with 128MB).
I don't know where Open ModPlug is at, but MadTracker 2.6 has a recorder (I haven't had a chance to actually use it yet since I tend to focus on Buzz) and supports ASIO. Depending on your machine specs though, you might end up with high latency issues.

Buzz is another one that I know supports realtime recording via ASIO, but Buzz is VERY system hungry due to the breakdown of synthesizers and effects (versus VSTi's which tend to incorporate basic effects into the synth for a more streamlined performance).
If your laptop can support it, I'd actually end up recommending MadTracker, since it's a child of FT2 (you already know all the effects commands) and supports VST clients without relying too heavily on them. That way you can start out with what you already know and add to it without having to change software. Renoise is another good choice for the same reasons. Both also have sample editors with all the basics like normalize/maximize, cut, paste, resample, etc., and you can apply reverb or other effects by using channel effects or aux sends.