I won't get into the financing part of it (different country).
We paid close attention to:
Dry basement - and if not dry then is there a sump-pump
Busy road - check during rush hour since the road may be a shortcut
Windows - old single pane windows are a heat sink, replacing all the windows in the house will cost a ton of money
Roof - when was it last replaced
Electrical - is it safe?
School system - this will closely affect the resale value
Insulation - is the attic insulated? are the walls insulated (a lot of older homes are not)?
Water drainage patterns - you dont want to be downhill from other homes or the road unless there is a really good drainage system like a french drain or a stream
Heating/cooling system - if it's old then be prepared to replace it. You'll save a ton on your utility bills
What we didn't care too much about:
Kitchen - if you care about the kitchen, like we did, then you're going to renovate it the way that YOU like it (ditto for the interior paint and floors)
Driveway - not that expensive here
Landscaping - if you care, you'll change that too
As my dad says, don't look at these things as reasons why/why not to buy the house - think of them as things that you may/may not have to pay to fix in the future. You can then use that to bargain for a better price.
Don't be fooled by "staging" when they bring in lots of plants and home decor stuff. None of that will be there when you move in

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See lots of houses, have fun!