Whatever amount you choose, make sure it's trivial compared with, say, the price of the character's next plus on his weapon UNLESS you as a DM are committed to making it matter to the game.
The key is that someone who is buying story items (ie - houses, boats, apple trees) shouldn't be penalised in combat for doing so.
Personally I wish there was some sort of advantage that a player could gain from these sorts of purchases: something like "You gain a story point. Story points can be spent just like action points, and you may spend a story point in addition to any action points during a single encounter, but not during the same round as an action point is spent. Only one story point may be spent per encounter. Story points recharge when you meaningfully interact with whatever it is that you spend the money on. You start with one such item, and may more such item per 5 levels, and the price is the price of a magic item of your level".
They also need some sort of major penalty for getting them hurt or damaged: ideally the DM should be able to potentially threaten the asset, and for there to be a real in-game penalty to it's loss.
So, at level 1 I get a story point and something that it ties to. I decide my adventurer has an elderly grandfather who used to be an adventurer, too old to adventure any more. We go off to slay the kobold menace, and during an encounter I spend 1 action point, then next turn I spend my story point. We have another encounter, and after that I get my action point back, but my story point is still spent.
We eliminate the kobolds and return home. I go and visit my grandfather, telling him an epic tale of how we vanquished the kobolds, and presenting him with a keepsake I took from the kobold leader. I regain my story point.
At level 5, I could buy another story item, but I choose not to.
At level 7, I spend the price of a level 7 item and buy a hunting lodge. I now have 2 story points, and whenever we have downtime, I go visit my grandad and tell tall tales, and then take some time off hunting in my lodge.
At level 10, I hire some people to maintain the lodge and train a cadre of rangers there. My downtime is spent visiting grandad, hunting and training new rangers.
At level 15 I choose not to get anything.
At level 21 I choose to build a hunting reserve, and buy 2 points at once.
And so on and so forth.