should I offer say $370k, or $365k or $395k?
It's worth $400-405K, in your estimation.
Obviously you still don't want to pay any more than you can get it for, but neither do you want to risk alienating the vendor with a cheeky bid. It's possible that a vendor who'd accept, say, $395K bid if it were a first offer (and somewhat reasonable), wouldn't accept $395K from somebody who started at $375K and worked their way up to that same figure. It's human nature - p*** them off and many will "cut off their noses to spite their face".
So I think you want to offer enough below your target that you have room to negotiate, but not so far below that you get the vendors thinking they'd not sell to you at any price.
Where is that figure? Presuming the market is warm (neither hot nor cold), I'd say somewhere around $390-395K, because I don't see the need to buy at rock bottom; anything below your estimated value you should be happy with.
But others no doubt would go lower to start with in order to try and secure a bargain, particularly if it's been on the market a while. On the other hand, if there are lots of potential buyers, you may need to go higher.
If they take your first offer, that doesn't necessarily mean that you've paid too much - it may simply mean that the vendors were prepared to accept a reasonable offer without mucking around. But if you're the kind who'd be annoyed if your first offer is accepted - even when it's below your estimate of the property's value
- then perhaps you need to start lower.