Only upgrade when something breaks, and that's only IF there will be a benefit to upgrading. A lot of upgrades a person could do could be a waste of money if you don't ride the bike more than 15 miles from home.
The single best upgrade for the money is buying lighter tires and tubes! And if your tires have knobbies on them and you never ride off road then get a set of smooth tires, get a set of tires that are not as wide, say your current tires are 42 then get a set of 38's for example. Cheap tires can weigh 1,600 grams each (just an example of 45 wide tire could weigh), whereas a good tire might only weigh 430 grams. Cheap tubes can weigh 250 grams whereas good tubes can weigh at least 100 grams less than that. I would start by figuring out what you can do with your tires and tubes as my first improvement.
Beyond that I would change out the rims, but personally I wouldn't do that either unless they broke or wore out.
So instead of upgrading to more expensive wheels and or components, or whatever, simply save that money and add to it for the next few years and buy a bike that you really want with the cash you saved from not doing stupid upgrades.
But only buy a new bike IF you "outgrow" your current bike. For example, you're constantly doing over 20 miles from home, and on weekends you're really going over that into the 40's and 50's miles from home. Once you start exceeding certain mileages then it becomes an issue with reliability, you don't want cheap Shiman Tourney stuff breaking on you when you're 40 or so miles from home. Also, when you do buy another bike there is no reason to get components better than either Shimano 105 or Deore (or SRAM equivalent) unless you decide to get into racing and even with 105 and Deore I know people who race on that stuff so that could be questionable, but something to consider if you decide to race. Always be reasonable when buying a bike, the biking industry wants you to spend a lot of money, and most of that money is for stuff that far exceeds most people's capabilities, so use common sense.