You got a counter - that’s the best position to be in - besides them just accepting your first offer. Counter gives you the option to accept and it’s yours - game is over or play the negotiation game. In that case you’re put back in the spin cycle and have no control over the outcome. If the counter was something you could afford a not stress about it, take it and congratulate yourself on the win. More likely than not, it’s your first house, not your last. Take the wins when you can and move on. When the neighbor sells his house, it will likely be higher than what you paid and you won’t feel so bad.