Buy and install the eSIM a day or two before you leave. You need WiFi to install it, so doing this at home is easier than fighting for a signal at Lynden Pindling International Airport. After you buy, you get a QR code by email. Scan it and the eSIM saves to your phone. It will not start using data yet. It only starts counting once you land and switch it on.
Pick your plan based on how long you stay and how much you do on your phone. A short city break in Nassau with WiFi at your hotel runs fine on the 1 GB for 7 days plan at $9.72. A full week split between Nassau and an Out Island fits the unlimited 7 day plan at $60.47, which runs at full speed up to 1 GB per day, then up to 1 Mbps. If you stream, share lots of photos, or travel as a couple sharing one phone as a hotspot, go for the unlimited 7 day plan with the bigger daily allowance at $105.74, full speed up to 2 GB per day, then up to 1 Mbps.
Make sure your phone is unlocked and supports eSIM. Most phones from the last few years do, including iPhone XR and newer, Samsung Galaxy S20 and newer, and Google Pixel 3 and newer. Keep your home SIM in the phone too. The eSIM handles data while your normal number keeps getting calls and texts.