So...
I have this 28" Nishiki hybrid that feels reasonably light to ride and cost about 300-350€. It's got stock everything. Straight hard rubber handlebars that tend to slide outwards and need adjusting back every few months, and "sweat" off little bits of rubber at old age. Tires are hybrid ones with a "plain" zone in the middle and grippy parts on the side that do not touch the road when you ride on a hard surface. Tire pressure is 4 bar. Brakes are "V" type and are adjusted correctly. I haven't really maintenanced the bike, just changed one tube when it went flat, re-attached a loose dirt guard with a ziptie, and put in some chain oil (one time in a few years).
High gears often do not settle down correctly but start to make noise; if that happens I switch back to lower gear and try again, but sometimes they don't work for the whole ride.
In addition to the bike, I have a helmet and a low-power bike mountable LED flashlight (enough for others to see me and for me to see the ground at low speeds), no other biking gear or clothing.
I tend to ride short distances (~15km), always going to some destination and not "just" riding. I ride in a relatively flat neighborhood. The top gear has been sufficient so far, but I'm not sure it will be for long if I keep riding. I'd like go fast, plus pull a longer distance now and then. It'd be interesting to be able to track my performance and bike's speed while riding, but I'm not sure how much I am willing to pay for that at this point.
So I wonder, what kinds of maintenance and/or fixes would I need to do to have the gears/chain work reliably?
If I want a better (= faster) riding experience, does it make sense to change parts on this bike or is it an equivalent of putting lipstick on a pig?
What comes to my mind is lock pedals+shoes, biking shorts and top, and maybe narrower tires if this bike can use them. Suggestions? In what order would you guys do improvements in this position?