Monero (Score 1)

Is getting into dealing with crypto currency worthwhile already?

Yes

Is Bitcoin the way to go, or will it falter under wide use / become easily trackable?

Bitcoin is possible to get and use anonymously (LocalBitcoins or some ATMs) but it is cumbersome to manage anonymity by default. Recommend buying a small amount of Bitcoin and converting it into Monero using Poloniex or ShapeShift.

What digital currency has the technical and mind-share potential to supersede bitcoin?

Monero is a very interesting crypto currency because it is based on mathematical proofs. The maths is too heavy for me but I believe its community has the mind-share potential to supersede Bitcoin.

Are there feasible cryptocurrencies that have the upsides of Bitcoin (such as a mathematical limit to their amount) but are fully anonymous in transactions?

While Monero doesn't have a fixed limit like Bitcoin does, some see this as an advantage. A common criticism of Bitcoin is what happens when all the coins run out; what if not enough people pay transaction fees and miners are not incentivised enough to continue securing the network. In Monero there's a small (0.3) block reward that continues to be issued. Monero does have anonymity and soon full anonymity with confidential transactions bringing anonymity to not only the addresses but the amounts too.

What are your experiences with handling and holding cryptocurrency?

Mined Bitcoin in 2011, invested in 2012, travelled the world in 2013 - 2014, got hacked in 2014, now using cold storage.

And does Bitcoin own the market or is it still flexible enough for an technology upgrade?

Bitcoin currently owns the market but I don't think the governance is flexible enough to upgrade to the anonymised technology that Monero uses - see block size debate.