How to obtain a good version of Pinocchio?

Short of finding a magical, perfectly preserved version of Disney's original Pinocchio and paying someone to master a DVD/BluRay/Digital copy from it, you don't really have many (if any) options and you're going to have to settle for something.

Low-quality VHS copies (and even DVDs) can't be made better quality.

If Disney decided to do some repairs to the film and fix the color, that doesn't mean it's inaccurate, it just means that, over time, the color in any film, regardless of how well preserved, will degrade and need to be touched up.

By the 1980s, it was becoming apparent that the collections of motion picture heritage were at risk of becoming lost. Not only was the preservation of nitrate film an ongoing problem, but the discovery that safety film, used as a replacement for the more volatile nitrate stock, was beginning to be affected by a unique form of decay known as "vinegar syndrome", and color film manufactured, in particular, by Eastman Kodak, was found to be at risk of fading. At this time, the best known solution was to duplicate the original film onto a more secure medium.

This does not mean that it necessarily significantly differs from the original. It's not the same thing as someone colorizing a previously black and white film. This is part of the normal film restorative process.

The article here on Wikipedia quotes several versions of the film:

With the re-release of Snow White and the Seven Dwarfs in 1944 came the tradition of re-releasing Disney films every seven to ten years. Pinocchio was theatrically re-released in 1945, 1954, 1962, 1971, 1978, 1984, and 1992. RKO handled the first two reissues in 1945 and 1954, while Disney itself reissued the film from 1962 on through its Buena Vista Distribution division. The 1992 re-issue was digitally restored by cleaning and removing scratches from the original negatives one frame at a time, eliminating soundtrack distortions, and revitalizing the color.

The more comprehensive digital restoration that was done for the 1992 re-issue was released on VHS in 1993, followed by its fourth VHS release and first release on Disney DVD in 1999. The film was not included in the Walt Disney Masterpiece Collection line, although early printings of the 1999 VHS did use the Masterpiece Collection logo. The second Disney DVD release and final issue in the VHS format premiered as part of the Walt Disney Gold Classics Collection VHS/DVD line on March 7, 2000. The third DVD release and first Blu-ray Disc release (the second Blu-ray in the Walt Disney Platinum Editions series) was released on March 10, 2009. Like the 2008 Sleeping Beauty Blu-ray release, the Pinocchio Blu-ray package featured a new restoration by Lowry Digital in a two-disc Blu-ray set, with a bonus DVD version of the film also included. This set returned to the Disney Vault on April 30, 2011.

If you want to pick one of these versions, you might consider the earlier restoration and go with the Walt Disney Gold DVD version from 2000. It seems they did another restoration in 2009 but I have no way of knowing which is more accurate to the original.

This site recommends a 1987 Laserdisc edition (assuming you have a Laserdisc player):

Pinocchio (1940): Color timing issues are the concern in the digital restorations and a negative impact on lighting depth. There IS a chance the restoration is correct. The problem is a lot of people feel that it is accurate to the cells but not how the animators expected it to look once transferred to film.

Purist recommendation: The 1987 CAV Laserdisc/1985 VHS (no DVDr preservation available).

Acceptable Alternative: The 1999 Limited Issue/2000 Gold DVD (which was the same disc repackaged and the same transfer as the 1993 CAV Laserdisc). It does contain some ghosting artifacts from digital noise reduction, but is generally clean and vivid.