Estimate oligo melting temperature with the Wallace rule and a salt-adjusted formula, plus a starting annealing range.
Under 14 bases the suggested figure is the Wallace rule: 2°C for each A, T or U, and 4°C for each G or C. At 14 bases and above it switches to the salt-adjusted estimate Tm = 81.5 + 16.6 log10([Na+]) + 41 × (GC fraction) − 675 / length, with [Na+] in mol/L.
Both numbers are basic estimates. IDT and NEB use nearest-neighbour thermodynamics, which this page does not. Use the annealing range as the start of a gradient, not as the temperature to commit to.
Which Tm should I use for a 20-mer primer? The salt-adjusted number, at the sodium concentration of your buffer. 50 mM is a reasonable default when you do not know. Wallace runs high on oligos this long.
How is the annealing range chosen? It is 5°C to 3°C below the suggested Tm. That is a place to start a PCR gradient, not a prediction of the single best temperature.