While custom-personalised calculations for your specific bike might be nice, they won't help the next person to read the answers. So a more-useful answer is to show the method.
Start by working out how many teeth your bike's cogs have. I googled up a plausible page which says:
- Crankset Shimano TY301 48-28T which is clearly a triple, so presume its a 38T middle ring.
- Cassette Shimano TZ500 14-28T and appears to be 14/16/18/20/22/24/28 teeth.
Poke these values into calculators like Bicycle Gear Calculator for a visual result like this:
There are two combinations greyed out - 28:14 and 48:28, or “small-small” and “big-big” respectively. These are “discouraged” because the chain has to flex most to get here. However, they work fine. [Comment of the original-post author: in practice, the bicycle rider hears noises while cycling with these and close combinations, and it's difficult to shift to such combinations; so no recommendation in practice.]
We see there is one gear combination that is an exact duplicate. 28:14 is the same as 48:24 which means you have the same cadence, or “pedal feel”. So which one you might choose depends on what the terrain is, along with the wind and how you're feeling. These are the “hardest easy gear” and the “easiest hard gear”.
It would be reasonable to think the middle chainring is useless, because the large and small chainrings have minimal crossover and you could do all your riding in those, and forgo a middle ring. (This is the basis for a sub-compact double chainring on some bikes.) However, your fast speed should be “comfortable” when into the smaller rear cogs. This lets you change up the rear-cogs for a stop or a climb without having to change chainrings.
Changing chainrings at the front is always a high-pressure event, because the chain is under tension at this point in the path. So you have to back off the pedal pressure to shift. As such, it makes the ride smoother to shift mostly at the rear, and only change at the front when you have to.
Your bike has 7 rear gears, so the common thought is that the middle chainring can get to all of them without undue wear. The large chainring can totally be used on the large rear cog, but its under the most angle so minorly increased wear.
Your bike appears to be lower-entry spec. Its not rubbish, but is also not a fancy expensive one. The bike does not have a cassette, instead it has an older design of freewheel (hence the 14 tooth minimum). Parts for this grade are common and quite cheap, so if you need a new $30 block of gears every couple of years, that's a tenth what a fancy road cassette could cost. Same goes for common 7 speed chain – it's cheap and available. Don't stress yourself about wearing out the bike's parts, which will take thousands of kilometres to achieve and likely years.
Personally I just ride the bikes, and make sure to clean and lube my chain periodically. This does more to extend the transmission's longevity than anything else.
