I guess you could argue that a boat is potentially safer. It's a lot harder to fall out of compared to a kayak
Forget budget and think about the sort of fishing you want to do. Then start investigating what you need to reach your goal state.
No good asking folks what you should be getting - that's your call and your spend.
Several things to keep in mind:
1. Whatever you are thinking of doing requires that you give something else up to do it (especially if you have a little one).
2. Setup budget is very different to ongoing running costs of your chosen hobby.
3. Cost out what you think you need to spend and then add a substantial contingency fund. If you end up not having to spend it, great, but the chances are you will.
Most of my fishing is quick dash stuff, where my daughter is off somewhere with her mother or she's in bed asleep being looked after by mum. That precludes my from buying into a kayak or boat or, at the very least, it makes things a lot more challenging, since a quick dash out the door in the evening, after 8pm, severely limits my fishing where either boat or kayak are concerned, but shore marks are still on the cards.
You need to figure out the kind of fishing you want to do and go from there.
Have a think about that yourself in relation to your own circumstances.
Good luck, whatever you decide.
If it was me I'd shove the 2k into a savings account for the little 'un
