What is the easiest way to find a Crashed Ship?
Find Transmission Towers, as every transmission tower leads to a crashed ship. How do you find Transmission Towers? Use the small, hackable red-beam beacons and search for "Transmissions." Eventually you'll get a hit.
Also, you can be "guaranteed" to get a 48 slot ship this way. There is a 1/3 chance that a ship you find will be one slot larger than your current ship, so just repeat that ad nauseum. I'm currently at 35 slots after my initial buy-in to a ship at 24.
Currently, there is an easy (semi-exploitable) way to farm for new ships. Unfortunately, there are a few notes to make first in regards to your question:
There is no such thing as a combat ship, at least in how the game currently stands. All ships move at the same speed and have the same access to weapon upgrades. The only way you would get a "combat" ship is by finding or buying a ship with a lot of weapon upgrades.
The second note to make is that finding crashed ships is a gamble; you will either find one slot less, the same number of slots, or one to two slots more. In my experience, this has been the case every time.
The biggest downfall here is; this exploit is being patched out very soon, so I'm not going to post the exact details of it.
As the game will soon stand, this will be the method to find ships:
Find a Korvax Transmission Tower (on Gek planets) or a regular Transmission Tower (non Gek planets).
Solve the puzzle inside the transmission tower. Usually it is a numbers puzzle or something similar.
Once solved, the tower will point you in the direction of a new ship.
Previously, you were able to use a Gek tower an unlimited number of times, with the same puzzle each time. I did this about 10 times per tower, and was able navigate with 10 crashed ship icons on my HUD. Again, this will be no longer possible thanks to a coming update, detailed here.
Basic Strategy
The easiest way is to use beacons which are located on or near many of the "points of interest" on the planet. (I'm talking about the beacons that have the orange beam of light coming from them, NOT the large pole beacons). When you find a beacon, you'll have to craft a Bypass Chip in order to use it. When you do, select to view nearby transmissions. You will get a new waypoint that will either lead to an Observatory, a Beacon (the pole kind), or a Transmission Tower. The only one you care about when looking for ships are the Transmission Towers.
Once you get a useful waypoint, make your way toward it. Solve the puzzle in the tower to reveal the ship's location, them had over to the ship. The number of slots in the ship you find seem to be directly related to the number of slots on your current ship - it will have plus or minus 1 slot.
That's the basic strategy of how to find crashed ships. It's tedious but it works, and it's a heck of a lot cheaper than shelling out 100+ million for a larger ship.
Optimizations
There are three ways to make this process a little less painful.
All Transmission Towers looks the same. What the building looks like depends on the home race of the current star system (Gek, Vykeen, or Korvax), but once you've found one TT, you'll know what all of them in the system will look like. As a result, you don't have to use the beacon to locate TTs - I often just fly around randomly until I find a TT, then land and collect the prize. Technically, this actually slows down the process, but doing it this way prevents your map from getting cluttered with waypoints you don't need, plus you get to do some sightseeing while you search.
There seems to be a bug with Gek TTs that allow you to "solve" their puzzle multiple times, thus revealing the location of multiple crash locations. Whether or not this bug will be fixed soon is unclear, so if you want to exploit it you should do so now.
You don't need to fix every system on a crashed ship - only the Launch Thrusters and Pulse Jets are required to fly a ship. This saves you some time and effort, since you can scrap/salvage all the other upgrades on the ship while you look for the next one.
Source: I found this info during my research for my question here.