28 is way too thin for the rebuildables you have bought recently, it is good for tiny coils for low Wattage MTL tanks but not much use for anything else unless you twist together several strands (if you look inside that wheel of 8 sets of coils you will see a section of 0.36 Quad core coils - they are made from 4 strands of 28 gauge twisted together which should give you an idea of how thin 28 gauge is). There are fused clapton coils made with 2, 3 and 4 28 gauge core wires and an outer wrap of much thinner wire, but this is pretty advanced coil building that requires advanced skills and power tools, so best left alone.
When you're new to making your own coils it is best to start with 24 gauge as others have recommended, after that maybe make twisted coils with a pair, or multiples of thinner 26 or 28 gauge together, none need any special tools - you can twist wire with a couple of sticks.
If you like fruit flavours I recommend starting with a spool of 24 gauge SS316L - a pair of 8 or 9 wrap 3mm internal diameter 24 gauge SS316L works really well - I wouldn't bother with 4 or 5 wrap type coils when using single strand round-wire, they are great for MTL but you need coils with plenty of cotton contact in DL rebuildables or you won't get enough vapour.