Your emphasis on immediate would not be mine. After all, I started out with no tools, so all the unfixed things were already unfixed, and could remain so for the time being.
So my hypothetical would differ.
And even if I wanted to fix those things, I could only do one at a time, so I would pick the most urgent, and get tooled up for that.
Still, I would look for used tools, deals, donations from family and friends and CL. I would even put out an ad on CL. I would let everyone I knew, and everyone I met, that I was looking for a, b, and c. I would print up a list with my contact info and post it and hand it out. I would hit all the garage sales.
And thus would acquire the things I needed in the order of most needed first.
A particular dollar limit would not be in place. Need, and available funds would rule.
Part of the problem that many of us here on GJ fall prey to, is the "collector" mentality.
We collect tools for a future need that may never arise.
We get on kicks about one type or color or brand of tool and collect them far beyond need.
We buy tools based on COO, or quality levels that exceed the need for the use the tool will see.
What kind of use, and what kind of user?
Putting a switch plate cover on, the cheapest screwdriver of the right size will do.
$1 China tools do a lot of tasks. I've found $1 China stocking stuffers from Lowes worked great. They included cutter sets, ASE and metric wrench sets, socket sets complete with ratchet and T handle bit sets. All found uses. A dollar won't get you a professional framing hammer, but it might get you something to hang a picture with.
So, for me, it has been a combination of cheap new, bought on sale, and better used tools that filled the needs.
As to specific tools, beyond buying to fill immediate needs, there are lots of guides online that tell what basic tools a household needs. Add to that list any tools specific to tasks the particular individual will want to attempt. It would be senseless to get automotive tools to someone who won't change a flat or do a brake job or change his own oil. Likewise, woodworking or metalworking tools shouldn't be in the possession of someone who won't use them.
Even home maintenance tools should match the abilities and inclinations of that person.
Some people should just spend the $400 on some good meals out.
And some people will spend it on the latest gold plated tool that they will never use.
Sorry for the non answer. It just seemed too broad a question, and kind of rhetorical..
Me, I have a little of everything, much of it unused. And yet I can never find the tool I need when I need it. And I always need a tool I don't have. Does that ever happen to you?
Bill