I’d definitely recommend using your card for online transactions for the reasons you’ve mentioned. I could have avoided fraud from PingIt & Tesco users could have potentially lost less money when the accounts were breached, using those two features. Plus, Amazon only charges you for an order when it’s shipped so that notification is nice to have.
I’d recommend sticking with having your wages paid into your legacy bank’s account for now, as you’ll probably have direct debits to pay from there. You could set up a standing order to then transfer that money to your Monzo card if you wanted to though.
I use Monzo for all of my purchases now, my legacy bank account’s bank statement is just a list of transfers to Monzo 
The features & things that I find Monzo most useful for are:
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Targets which have been invaluable, in terms of giving me a sense of what my money is being spent on each month and therefore, what I need to buy less of and how much I’ll probably spend on each category in the remainder of each month.
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The Pulse Graph - comparing the gaps between my top ups (which are always for the same amount & are supposed to be enough to cover my spending for a week) this month vs previous months, to get a sense of whether I’m spending faster or more slowly than usual.
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The ‘live’ transaction feed, to see how much I spent last night, on a night out (so no dreading pending transactions, although it’s usually painful to see).
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And of course not having to worry about exchanging money (& getting a terrible rate) before travelling abroad, as there’s no FX / ATM fees
To find out what features other users find most useful, it might be worth checking out the Monzo Love Tweets Twitter account which often shares tweets from users who’ve discovered features that they think are particularly great (as well as praise for the customer support team’s rapping skills)
And lastly, if you want to know more about Monzo, you might find this post useful -