You have totally the right idea hun. Mash with fingers will be messy, but a huge part of her learning about food is the texture etc, and playing with it is an important part of the process.
The best way to avoid constipation is to make sure that her milk intake doesn't drop. Some mums find that potato, banana and beans can cause constipation, but I don't think you need to avoid them altogether - she will only be having small amounts for a while so give things a try and if it seems to cause a problem then you give that food a miss for a while.
I don't think I had any problems with stained nappies - although I imagine beetroot could be interesting!
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