Supposing you start with enough Precursor anomalies nearby to make investigating them without medium hulls worthwhile, what are the best options? You can't get too distracted with military techs for this purpose, without any other threats to bother you it's better to focus on other technology categories. The right combination of mercenaries can work, but that's going to eat a ton of credits.
I find that with 6 techs, you can have consistent success. You'll want orbital manufacturing (and its two prerequisites) for small hulls, then militarization, weapons systems, and defense systems. The survey ship you'll be using for any of these solutions is a small hull with 3 deflectors. The shields might technically be unnecessary for your unarmed survey ship because attackers wouldn't usually attack it until everything else is dead, but better safe than sorry.
For the minimum tech approach, make 4 more small hulls with sparrow missiles and 3 deflectors to accompany your survey ship. At Incredible difficulty this gets consistent success, though some of the time you get bad luck and suffer some damage, or even a lost ship. Adding a 5th missile ship seems to guarantee success, but requires a logistics bonus (possible from tech, race, or a Precursor anomaly reward).
By researching a 7th tech (beam weapons), particle beams are a viable alternative if you can find elerium, but not antimatter. However, swapping sparrows for particle beams doesn't save enough mass to add another shield (without additional bonus mass from race or another tech). I'm sure there are edge cases where particle beams make sense, but if you're willing to research a 7th tech for this purpose, I'd recommend going the kinetic route.
By venturing up the kinetic chain with your 7th tech, superior railguns achieve very consistent success in my testing. As a bonus, these require no special materials. You can fit 5 deflectors and a superior railgun on a small hull without any other sources of bonus mass (more tech, race, etc). With a 5 ship fleet (1 survey, 4 railgun) I went more than 20 anomalies in a row and never saw a ship take damage.
Once you've obtained all of the easily reachable Precursor anomalies, it's probably prudent to wait until you have medium hulls to go after more. Disband your survey fleet, and maybe upgrade the survey ship to a variant with engines and/or life support to scoop up unguarded anomalies. Garrison the warships at planets so that solo transports can't conquer your worlds. In fact, if you're not putting a ship at every planet already, it's a good practice to have. I like to equip a cargo hull with the cheapest laser and put one at every otherwise undefended planet. If you have spare thulium, a cargo hull with a basic railgun will be built slightly faster.
Anyway, by the time you have medium hulls, at minimum, you'll be able to fit a superior railgun, field generator (+5 shield to all ships), stellar accelerator (+2 speed to entire fleet, costs 1 promethion), and 4 stellar support modules on a medium hull. Make 4 such ships, and a 5th that swaps out the field generator for the survey module. You can also remove the railgun from the survey ship and replace it with whatever you want, the extra firepower isn't necessary for anomalies, but for hostile enemy fleets it may be useful. If you want to get even stingier your survey ship can be a cargo hull, but with only 3 hit points, I always get nervous knowingly putting frail cargo hulls in dangerous positions. Now you have basically the same firepower and shields as before, but your ships can go further and faster. If you want the fleet to go even faster, add a commander. If you want yet more speed, make tiny hulls with nothing but a stellar accelerator and life support modules and add them to the fleet. I believe the only relevant unique equipment you could get from a colonization event for this fleet would be the subspace splinter.