What is the best way to expand your exosuit inventory in No Man's Sky?

Inventory slot expansion is based on two factors: cost and time efficiency.

Upgrades can be acquired in two ways: for free, by repairing a Drop Pod expansion terminal or by buying them from a specialist on a Space Station OR the Anomaly.

The first strategy technically requires more time as you have to find the pod and repair the terminal be able to get the upgrade. Yet, both the two task can be made far more efficient:

• Drop pods can be found by using a Drop Pod Coordinate Data and a Signal Booster. Data can be farmed relatively easily by buying them from vendors and as a reward from some missions, most notably the Nexus ones on the Space Anomaly.
• The repair of the terminal always uses the same materials (currently as of the Expedition update should be 10 sodium nitrate, 1 carbon nanotube and 1 antimatter housing) so you CAN prepare those before getting to the pod.

The second strategy requires to do some system hopping since you can only buy a single expansion on the system Space Station (and the is assuming there is an active one in the first place - avoid Abandoned and Uncharted systems!) and another one in the Space Anomaly (yep, the Anomaly offers one upgrade per system - multitools on the Anomaly work in the same way).

Now: what is more efficient? The relevant thing to notice is that bought upgrades prices scale FAST. Cargo slot prices for example go from 50,000 units for the first slot to 1,000,000 for the last one (see the table on the wiki for additional info and numbers). Fully upgrading the inventory costs 45,555,000 units.
This means that unless you already have access to good money making resources the more cost effective strategy is:

• buy the first upgrades from space stations and the Anomaly
• as soon as the prices scale over the average price for a Drop Pod Coordinate data (about 100,000 units) switch to those.