Buying a bandsaw or scroll saw can be quite an expensive investment, but if you already own the inexpensive classic jigsaw you can convert is to a vertical saw very cheaply and extremely easy.
1. Using some scrap MDF that I had laying around the garage I build an open box 43cm (Length) x 19cm (width) x 27cm (height).
2. I dismantled the sole of the jigsaw and drilled 3 hole in it. The diameter is 5mm because I had some bolts laying around.
3. Put the sole on the inside of the "table" and mark the three holes. Then drill them and sunk the head on the top so the head of the bolts will not bother us. Also mark and drill the position where the blade will be.
4. Put the sole back on the jigsaw and attach everything to the table.
5. Good luck !
6. If you know you have a tendency to stick your finger in the eye, or you are a complete moron when it comes to using powertool please don't do this modification. You will only manage to hurt yourself very, very badly. The machine has no cage and extreme care must be taken when operating it. Please don't blame me for missing fingers :)
As a possible modification you can make the table wider and longer. Also, bolting the table to you bench might be a very good idea as from the vibrations it tends to be a little "jumpy" adding to the above mentioned risk.
Have fun and stay safe.