Anything to suggest? Always, my friend with beard
I'd suggest push ups with wide and narrow grab, wide is better for chest and narrow is better for triceps.
And if you are gonna buy dumbells what would be really cool, there would be dozen of things what you can do with those. With dumbells you could train back muscles, biecebs, triceps, shoulders, chest.
If you are gonna get those dumbells, I suggest you to buy those where you can change the weight of dumbell by changing the "weight discs" or what ever they are in english. Because every move can use diffrent weights, like you are maybe gonna use diffrent weights when doing bench presses with dumbells and when doing bieceb exercises.