A few places I've looked have said I have to order and pay online and collect euros from branch. I'm not comfortable with this
Why not? It's perfectly safe if you use a known provider.
I just want to go somewhere with my money and leave with my euros
You can do this at banks, post office and bureau de change, eg in many large supermarkets, M&S etc but it will cost slightly more. You may decide it's worth the extra cost, which will be minimal if you plan to use your card most of the time.
For most places in the Eurozone you don't need many euros any more. Just like the UK, it's easy to get away with little or no cash in most circumstances in many places. Just make sure you understand the ins and outs of card payments as there are some cards that are very good for overseas spending and some that are very expensive, especially if you use your card for every last coffee, lunch, ice cream and bus ticket. Have look at:
www.moneysavingexpert.com/travel/cheap-travel-money/
But these days we take a token amount of euros (max 50-100 or whatever we had left from last time) and use our cards most of the time.
However, we try to cover all bases because some places are still cash only. eg, we recently went to Menorca for the second time this year and confidently waited at the bus stop with our cards and no cash only to find that the bus was cash only, despite the bus we used the previous time taking cards, and possibly being card only. So we had to walk the couple of km to the main town, so we could get some cash.