You definitely need a basal thermometer. They are calibrated to read very small temp changes. I only spent about 8-9 dollars on mine. It is digital and has memory, so I can wake up to take my temp, then turn it off and go back to sleep. When I am ready to chart it, I turn it back on and it shows the last temp taken. Good luck charting!
The only basal thermometer available to me locally read temp to one decimal point, and was accurate plus or minus the same amount as the regular digital thermometer. But it cost way more, like twice the price. I bought the regular thermometer. So far I've managed fine with a regular digital thermometer. My charts clearly show a temp rise at ovulation, so far anyway. Been using a regular thermometer for 30 cycles now.