Hi & welcome! And kudos to your efforts to garden 'cide free! I don't use any and have very few, isolated issues that I deal with manually if I decide it's necessary.
One thing to remember is that it's not necessary to "do something" every time one sees an unwanted visitor on plants. Of course you're not going to let something ruin your only copy of something expensive or sentimental. But as long as no serious damage is being done, leaving things alone can be the best plan because predators need something to eat. Without any pests (food,) beneficial predators can't & won't establish a presence.
If I go to the effort of removing some kind of critter big enough to fling, like a slug or caterpillar (that's not destined to turn into a beautiful butterfly or beneficial moth,) I try not to kill them, but fling it away from desirable plants so something can make a meal out of it.
Whenever you find something mysterious or concerning, figuring out what it is is always the 1st step to deciding the best course of action. Just like you've done by posting your pic here. Well done!
In your pic, it's clear to see where the aphids are. It's your call if you want to cut off a flower to cut off the aphids, but know that if you can see where pests are, cutting little bits off of plants to get rid of them that way would be a fine thing to do on almost any plant. You're welcome to ask as many questions about as many plants here as you want. Have fun!
so much! Very new to gardening, how relaxing is this!. I will definitely look for these products. 
