That CPU won't bottleneck the Ryzen 5 1600 so you're good with that.
1440p will be great on a GTX 1070.
No you don't need a bigger power supply, 650w will be more than enough for a 1080 ti.
And if you can fit an SSD in your budget then definitely, HDD + SSD are a great pair.
Usually SSDs are used to store operating system and a few games to improve boot and loading times.
Should i think about an i7 770k over the ryzen 5 1600? is the extra 100$ worth it and will it last me? Could you recommend a sort of budget ssd and an hdd?