Well, there are some facts to consider here:

1. DVD resolution is substantially lower than, say, a 1024x765 screen capture. Small text that is legible on-screen will not be nearly as clear at the reduced size.
   
2. Premiere's scaling is a bit soft, so text will be even less legible than it may be otherwise with better scaling algorithms.
3. Over-sharpening in an attempt to make the text more legible can cause "buzzing" – particularly on interlaced display, which can look even worse than blurry text.
4. Super-sharp text does not tend to compress well to lower bitrate MPEG-2.
5. Since the aspect ratio must be changed, you cannot preserve the original pixels or perfect sharpness, since some scaling will always be required.
   

So, if it can't be too soft and it can't be too sharp… make it larger. Here's what I do:

Preparing the Captures:

1. Use Techsmith codec to capture.
2. Open the Techsmith AVI in VirtualDub
3. Go to Video / Compression and choose Lagarith lossless codec. Made sure that it is set to RGB and null frames are enabled (checked)
4. Add Video / Filters / Resize and set it to Absolute: 2048x1530, filter mode: Nearest Neighbor. Here, you are using "point resizing" to double the image size while maintaining maximum sharpness. The kind of resizing does not usually work well for photographic images, but it is ideal for screen captures: maintaining the sharp, boxy look of non-antialiased text. It will help us from losing too much detail when the video is scaled down later on.
   
5. File / Save as .avi from VirtualDub

Cropping, Scaling and Filtering the Captures in After Effects

1. Open After Effects and create a composition that matches your intended output (such as 720x480, DV aspect ratio, 29.97 fps, etc.) and set it to the length of your screen capture.
   
2. Place your (very large) AVI on this timeline and scale it to fit within the safe area (something like 25% of original size), call this composition "establishing_shot"
3. Create a new Adjustment Layer above the main video track. Apply Effect / Blur & Sharpen / Fast Blur to the Adjustment Layer (Blurriness=0.5, Blur Dimensions=Veritcal, Repeat Edge Pixels checked). This is to soften it a bit vertically to prevent issues on interlaced screens.
   
4. Duplicate the "establishing_shot" comp and rename the new one, "medium_shot"
5. Modify the scaling of the AVI in the medium shot to approximately 45% of original. Add motion and/or scaling keyframes to keep the focus loosely on the main action on-screen; such as the area where the mouse pointer is. (You may want to set the keyframes' Temporal Interpolate to "Hold" so it will simply cut to the action instead of trying to animate all of the panning.)
   
6. Duplicate the "medium_shot" comp and rename the new one, "close_up"
7. Modify the scaling of the AVI in the medium shot to approximately 75% of original. Add motion and/or scaling keyframes to keep tight focus on the action.
8. Render all 3 comps from AE as either DV (for better editing performance) or Lagarith (lossless quality)

Editing in Premiere Pro

1. Import your 3 "shots" into Premiere and place them in a Multi-Camera sequence
2. Nest the Multi-Camera sequence in your main timeline and switch back and forth between the 3 views as needed

So, the "establishing shot" will show them the entire screen. Small text will not bet legible, but it will give them a good idea of how things the screen is laid-out. The "medium shot" will let them see text fairly well – and it allows them enough space to see how the "focused" text relates to other elements. Finally, the "close up" will give them the best view of individual menu items and buttons; showing how things highlight when clicked, etc.

Preparing the Captures:

 

1. Use Techsmith codec to capture.
2. Open the Techsmith AVI in VirtualDub
3. Go to Video / Compression and choose Lagarith lossless codec. Made sure that it is set to RGB and null frames are enabled (checked)
4. Add Video / Filters / Resize and set it to Absolute: 2048x1530, filter mode: Nearest Neighbor. Here, you are using "point resizing" to double the image size while maintaining maximum sharpness. The kind of resizing does not usually work well for photographic images, but it is ideal for screen captures: maintaining the sharp, boxy look of non-antialiased text. It will help us from losing too much detail when the video is scaled down later on.
   
5. File / Save as .avi from VirtualDub

Great, thank you!

I got through that part, but as for After Effects, I cannot get a trial because it says I need 64-bit, and I guess I have 32. Is there a way to do it without After Effects, or should I purchase it? I wanted to make sure it worked before buying it, but if there isn't a way to do that, it may be my only option.

Thanks!