OK with 350 names in my database the FTM software is suggesting that I upload it to their site. I suspect that this is just a cheap way of extending their data source.

Do you have any experience or advice? Should I publish or not? If so which sites are the best?

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Pone ubi sol non lucet!

The only place I think about putting my tree on is Genes Reunited. It's password protected and if people want to look at your tree, then you have to give permission.
I've got the tree on my own machine though. I certainly wouldn't put it anywhere that is accessible by others willy-nilly. You can also put it on Ancestry.co.uk but I don't know how well protected that is. You certainly don't want living people on a publicly available tree..that's a recipe for identity theft.

what about Tribal Pages. It's got a free basic level, you can password protect it and only edit it yourself and also you can set it so you can just view it yourself or invite other people to it.