After you add a few things to it from surveying anomalies results, the Discovery can become good enough to take on the "lightly defended" anomalies, from those you can sometimes get some small or tiny warships or warship designs to rebuild in your shipyard to add to the fleet. You particularly want to choose the Field option for the 3 way defense item choice as an upgrade. It adds 4 to Shields of ALL ships in the fleet, including any cutters/gunboats/etc. that you add from the lightly defended. You have 10 Logistic Points and the Discovery uses 6 of them, that means you can add 4 Points worth of warships, probably 2 two point ships. You can also get Small Ship Designs that you can rebuild (one of) in your shipyard, that will have weapons that you can reinforce Discovery with. Once you have 1 or 2 Field upgrades you can also start taking the +6 to Armor option also. You will also need to add some more weapons to the Discovery as well as defenses.
It is also not too hard to add another 4 Logistics Points via Tech for another 2 small warships. After that and 2 or 3 of the Field Upgrades to +8 or +12 (Shields) and +6 or +12 to Armor to all Ships, and you have a fleet (Discovery + 4 Small ships) that might be able to take on the "heavily defended" anomalies.
Once you can Build Small Hull Warships, you can design a Fleet Support Ship that gives a 4 to Shields AND a +6 to Armor to ALL ships in the Fleet in ONE Small Hull. The +6 s to Armor are needed against Space Monsters and Precursor Ships.
You can also rather quickly at the beginning of the game, design and build TINY Hull Fleet Support Warships that give either a +4 to Shields OR a +6 to Armor to ALL Warships in the Fleet. They can make other ships a lot more survivable when they join them.
So they ARE ways to help yourself against those random Pirates, Space Monsters and Precursors. It will take some time but it can be done.
Do NOT forget to add the Infinite Range Mercenary component to ALL designs, it does NOT use a SLOT.
P.S. When you win a space battle sometimes you will get a piece of equipment for your ship. In fact when I have had multiple ships fighting multiple ships, I have had 2 ships get something after the battle was over.
P.P.S Rename ALL of your ships so when you get a message about something happening to a ship, you know WHICH ship it was/is. I just add a modifier to the design name, e.g. add a 1,2,3, etc. or a,b,c, etc. The IS matters when you have to make a choice to keep or sell something, or which of several options to choose from, such as shield, point, or armor on the defensive item your get fairly often. Some items I tend to sell rather than keep.
P.P.P.S I like to design and build (a lot of on the larger Map sizes with many Sectors to explore) a Cargo Hull Surveyor that has weapons and defenses so pirate snipers can not kill them.