Oh, my goodness...the dreaded sticky tape!
If you could only see the damage that old sticky tape (and I'm talking anything from 10 years old upwards) does to paper, you would swear off using it on anything important. See here for a couple of examples:
http://aiccm.org.au/index.php?option=com_content&view=category&id=3&Itemid=30Likewise laminating. It melts plastic into the fibres of the paper and is irreversible. Down the track the plasticisers start to migrate through the plastic and cause staining and stickiness and as time goes by, documents will be ruined. Horrible stuff.
There is no need to go down either of these roads. If you don't wish to invest in the services of a conservator who would repair the paper using strips of fine tissue and a reversible paste made from wheat starch, you could simply photograph or scan the pieces to create a digital image of the original document, then store the pieces all together in something as simple as a "zip lock" plastic bag that you can buy at the supermarket.
There are plenty of simple preventive conservation/preservation ideas on the AICCM website linked to above, and other professional conservation organisations around the world (such as the UKIC, AIC etc.)
Cheers
Prue