What matters is what the property is worth. What's its value? You can determine that from the comps. A Realtor can supply you comps.
Once you know what it's worth, that's your ceiling price. You pay no more than that. So, for negotiating purposes, your probably offer less. How much less?
Well, if the comps come back at $400,000, and the property's listed at $375,000, you may want to come in near full price. Note: I said "near." Offer full price, without negotiating, and many sellers will wonder if they've done the right thing. ("Gee, I should have asked for more.") If the property's listed at $400,000, pretty much the same answer: come in somewhat below the listing price.
And if the property's listed at $425,000, you come in somewhat below the comp number of $400,000. How much below? There are a couple of possible strategies. On the one hand, you can make a real solid, "best and final" one time offer of, say, $395,000. Or you can recognize that in the United States, many people tend to "split the difference" in an extended negotiation. (And not just money: Look at the apportionment of Democratic delegates from Florida and Michigan...half a delegate. Now that's "splitting the difference"!) So if you're prepared to negotiate, and recognize that the owner might simply reject your initial offer, if he's priced at $425,000, you offer $375,000 and you'll probably end up around $400,000. Or start a bit lower, and maybe end up below $400,000.
Final point about such negotiations. Don't offer a nice round number like $395,000. Make it odd: $394, 805. When the listing agent asks your agent where that number came from, the answer is: "That's what my client calculated the value to be."
You also asked whether there's a difference if you're looking for a single family home, condo, or some other type of property. No. There's no difference.
Hope that helps.