A table saw cuts up from the bottom of the board, pressing the board down towards the table ...at least at first. A RAS cuts from the top down, lifting the board off the table ...at least at first. Table saw blades have a "positive" hook angle or rake, so there's no problem. The RAS will also cut with a positive hook angle, but its a very aggressive cut and will tend to self feed into the work. That's why you have to use a firm control when using a TS blade on a RAS!
A proper RAS blade, now available with a "negative" hook angle, however those were not made back when they initially came out with the home shop versions of a RAS. People were not aware of the self feeding issue and made mistakes which sometimes resulted in injuries.
To the poster's original question, I'm of the opinion a table saw is central to a woodworking shop. If the budget is limited, then I would say any table saw is better than none.
Why? Because you simply cannot beat a table saw for precision and consistency. Hands down, only the best commercial grade radial arms can compare in this regard.
The common RAS's for homeowner use are not reliable machines. The settings are easily disrupted. For example, one bump of the arm will require a recheck for 90°.
IMO they are one of least safe machines because they are so prone to self feeding and binding. I would never even attempt ripping on one. Sliding miters have largely taken their place.
That said, I have one and use it a lot. 95% for rough crosscuts. I use a miter saw for precision miter cuts and small pieces of wood, etc.
I have probably done more ripping on a RAS than anyone on this forum.
I have done a whole lot of ripping with a circular saw over the past 50 years. I have done a lot more ripping on the table saw than either of the other 2 saws, probably several thousand linear feet. I know what I'm doing.
I also know what happens when a rotating circular saw blade enters the wood and starts to cut and that depends on the type of saw being used.
Let's start with a hand held circular saw, a very common tool that just about everyone has used. The saw has a base plate to support it's weight AND to press against the top of the workpiece, very important. You would NOT just freehand hold the saw above the work and attempt to saw with it! As the rotating blade enters the work the teeth are rotating upwards, pressing it against the base of the saw. You can now control the forward motion and continue cutting with no issues, including no kickback. Depending on the material, plywood or lumber, the saw kerf may close up and bind the blade, stalling the motor. Plywood will NOT do this because it's homogeneous, lumber will because it's grain varies within the wood.
Now what happens when a miter saw is used? As you start the cut you are pushing down. The saw blade is entering the material from the top, BUT you need to hold it down against the table and the fence with your left hand. You can't just lower the blade without a secure grip on the workpiece or it will tend to lift up because that's the direction the teeth are rotating.
Now what about a RAS? It's very similar to the miter saw in that the rotating blade is above the workpiece, except you are pulling the saw towards you from behind the fence. As the teeth enter the material from ABOVE, it's being pressed down into the table and against the fence, BUT you still need a firm grip on both the material AND the handle on the saw. Depending on the hook angle of the blade it may self feed aggressively into the material. Here's where a negative hook angle blade is the best type to use on a RAS.
What about ripping on a RAS? It's a lot like a circular hand saw, BUT there is NO base plate to keep the material pressed down while the blades teeth rotate upwards, lifting the material. This is where the blade guard/cover must be used to prevent the material from lifting upwards! This is very critical and often not done. It's the main reason for kickbacks and lack of control of the material! I used a roller located right above the material when I ripped several hundred feet of Cypress for this barn door project:
The roller prevents the workpiece from rising upwards due to the upward rotation of the teeth entering the material.
What about ripping on the table saw? Now the rotating blade is entering from BELOW the material. The teeth are pressing the material downwards, at first as they begin to cut then under feeding pressure. As the kerf is opened up there is some tendency for the material to be lifted up at the rear of the blade, BUT not much because it's not cutting, just friction on the sides of the blade. If the kerf closes because of the internal stress being relieved, the friction is greatly increased and that's when the material will lift up and either stall the motor or cause a kickback. A splitter or riving will prevent this from happening, it's is a critical table saw safety feature and should always be used when ripping.
So, some basic physics is needed to understand what's happening when a rotating blade enters the material from above AND whether there is a means to prevent it from lifting upwards, like a base plate on the circular saw, OR a blade guard/cover on the RAS.
Table saws are different since the material is resting on the table initially and is being pressed downwards as the cutting begins. There is only sideways friction if you stop feeding the material forward.
A bandsaw has a much smaller blade contact area and the teeth are offset leaving the remainder of the blade in the kerf, therefore with much less friction. The material is being pressed downwards onto the table the same as the table saw, however. Bandsaws will not kickback because unlike a circular saw the width of the blade plane is so much smaller. For this reason on a table saw, any rotation of the workpiece away from the fence at the rear while the blade is cutting will bind and cause a kickback.