Image wise Photoshop. Or alternatively GIMP is a free and more than adequate replacement for most people's purposes.
For video Abode Premiere. Fairly intuitive timeline based editing and links handily with Photoshop for bodging stuff back and forth. Not very familiar with what alternatives there might be tho so probs someone better to say than me.
If by Photoshopping you mean major changes like cutting things in and out of images, Photoshop or GIMP as Carel said. For touching up photographs though (contrast, vibrance, brightness, hue, straightening, cropping etc) Lightroom is a lot quicker and easier.
You can get both PS and LR on the Photography plan from Creative Cloud. About 6 quid a month I think. Depends on your needs whether it's worth it.
That wouldn't help with the video stuff though, of which I am clueless about.