For building muscle, and to see results quickly, you need to start using the heaviest weight you can manage a 'set' with. I didn't know that, when I started, and I started using a 2kg dumbbell, but it was too easy. I'm now using dumbbells at 5kg, that's about my max for a set of 10 reps on, say, a single arm tricep extension. You should really find the last rep difficult but still be able to complete the move with good form and without hurting yourself.
For bicep curls, however, the 5kg is quite easy, for me: I could easily move up to a 10kg for a set of ten reps, but there's no way I could do a 10kg x10 reps set of tricep extensions, so I've opted for the 5kg for now. I just increase my reps on a bicep curl set to 20 instead.
It mainly depends on your current level of fitness, and your current muscle mass, though. I don't think 2kg is much use, unless your arms are like twigs. Yeah, good for toning, if you perform a million reps, but rubbish for building. I'd suggest starting with the 5kg, as you've probably already got a good upper body strength if your mucking out horses, hefting hay bales, etc.
I also think you're better off going through the whole range of exercises you'll be doing, first, with the heavier weight, and if you find one of the exercises more difficult than the others, use the hardest to perform exercise as your base point. Take off a kilo, maybe two, if the weight is too heavy, and then strengthen the 'weakest' muscle first, so to speak.
I also think you're better off buying a set of bar and lock type dumbbells, and then you can always add/buy more plates later, and increase the weight easier, rather than buy one of those 'cutsie' rainbow coloured 'fixed' weight sets which might be too light and which are quite expensive.
In a few weeks, I'll be increasing my dumbbell weight to 7kgs. It gets easier, quickly. And my arms? They make men weep bitter tears of jealousy. I am struggling, though, to buy jackets: the arms are just not big enough, these days.