The Ultra probably doesn't have a DVD drive, at best a CDROM drive, so any Linux disc would also have to be a CD, not a DVD and that would be something like Lubuntu on CD. Most other Linux distros today are DVD, other than some of the really stripped down versions like Puppy, and DSL.
The only way you can easily get Linux is to download the ISO file, "burn the image" to a CD yourself, or purchase one already made. The lowest price from a reputable place that most linux distros have a working relationship with is http://osdisc.com There are other places that sell linux discs for low price, but you also want to make sure you get linux from a trusted source, as for any software. You can read more about various linux distributions at http://distrowatch.com
As for these two computers your family stored, have you gotten permission to mess around with them? Reason I ask is they may have personal data on them your parents want to keep such as pictures of your family over the years and they'd not want to chance losing that information. Hopefully they backed that up years ago, but some people figure it's on the computer they shove in the closet and will be there later, and just leave it that way. Before you mess around too much on them, make sure with your parents there's nothing still on it they don't mind losing.
This is what Dell shows for that Dimension computer model number. Seems wrong to me.
System summary
Service Tag 3446C
Computer Model 4xx/P, 4xxs/P, V4xx/i, V4xxs/i
Shipping Date 10/29/1993
Country United States
But if that's true, then it's probably pre windows 95 system on an old 486 motherboard, those came as 486SX and 486DX and ran at 33 Mhz speed with the fastest being a quad speed. If so, the the Ultra is your better computer there.