Back in the dark ages, when I was young, I made a deliberate decision to invest in tools and learn to repair & maintain my possessions - very largely motivated from numerous experiences with "professionals" charging for repairs which failed and I had to (re-)fix myself. Some 45 years later, in summary, this has been very wise/profitable BUT I have advised our kids not to bother following my example, as recent production tends to fail sooner, but not be repairable (due to design, short service life, super-cession, lack of parts, or not being worth the effort). While I work as a professional, I paid my way through university as a (trained) car mechanic, and have taken formal courses in diverse fields, as well as the learning that experience forces upon you.
When confronted with a fix or replace decision, I tend to be pretty rationalist (except in the case of sentimental value stuff, where over-capitalisation is not part of the decision). I tend to dismantle or otherwise investigate (eg, test) just far enough to get a clear picture of what is really the issue to be fixed (NOT farther). I then sort out the likely cost of repair (eg, special tools, parts if available) vs what I estimate the remaining value of the item is (in current dollars, not what I paid for it)(add time in as you value it). Whatever people tell you, there is always a risk inherent in any repair that things will come unstuck (demonic intrusion!), so there really needs to be considerable daylight on the "value" side. Quick examples: (OK but not great)Our Maytag washer survived 20 years of 3 wash a day use (think too many children), then the transmission froze. Repair was $240(my cost) vs estimated remaining value to us of $400 over 3-5 years. In the event, it went just over 5 years. (great) Our old Sunbeam Mixmaster went 30 years before a tempered part of the controller broke; no easy replacement parts or repair to the metal, so I found a used head on Ebay for $15 after looking at (terrible) reliability reviews for the new $300+ replacements - working perfect 6 years on with excessive use. On the other hand, with phone/tablet progression, even replacing a battery in an older unit can be a poor investment.
My perception is that current manufacturing seeks to turn "durable" items into "consumables" which they can bank on having to be replaced sooner rather than later ... good business model but a waste of time and resources for me. Hence, I advise our family to begin with the end in mind, and buy the highest quality (based on actual independent product reviews, not advertising) they can find - which also tends to mean better warranty and longer parts support. Finding truly skilled and honest (repair) artisans is hugely difficult - my list of those I would recommend is not long - and if you use word-of-mouth be sure to ask till you get multiple recommendations (ie, weeding out "my drinking mate" or cousin). I know my personal limitations, so while I will do prep work for panel beating, I leave the spray work to someone with a "good (great) eye" for painting ... in my experience this could be as low as 10% of painters. People like to make a lot of money, and it isn't just the car game where "over-servicing" (replacing parts that don't need it) is common - hence the need to have a clue what the actual problem really is ... otherwise (for example) your gas hot water heater may be replaced rather than have a $40 part changed so that the "disposed for you" unit can be sold on to someone at another job.
To make any decision like this, you need information (duh). Information comes from 3 sources: repositories (eg, manuals, web - especially specialist discussion threads), experts (sometimes available through the web, but generally more time and $ to access), and research (DIY, with big time and $ costs - best not go there unless forced). Older manuals contain more gold than newer (think: litigation). Also, the web is now by far the biggest example of "a little knowledge is a dangerous thing". People with that limited knowledge/experience feel a need to share it, often in totally inappropriate situations. Before embracing some quick fix brilliance, look to see if others have "thanked" the poster because their advice actually worked - if not, keep looking (in my experience).
One final piece of wisdom from 45 years of fixing: HIDE your abilities and experience! Otherwise, you will be assailed by people looking to "borrow" tools, dump every broken item they ever have in your lap, then come back after you kindly changed a globe in their car to tell you that the transmission is gone and "you were the last one to work on it." If you can't help yourself, swear them to secrecy once the job is done! Seriously!