That's sort of like this: When I was 16, I bought my first car. $75. If I were buying my first car today, with a little hindsight, I'd buy a new Range Rover. Spend the extra the first time.
So, OP, does it matter? Only if you can afford to throw $500 on a press that no one has convinced me makes better ammo, or is so much easier to use, or is such an orgasmic pleasure to use over all the rest.
I drive a 1990 F-250, my buddies drive new trucks with every gadget known to man. Yep, I do like the fact that they don't need to get out and lock their hubs manually, but it's not like the truck drives itself or loads the groceries for you. It's a truck. Goes from A to B and I'm not willing to spend 20% of my pay for the next 5 years paying for that. Your level of comfort determines your purchase. Much the same with everything in life.
You have not told us your end goal with reloading. Is it plinking, hunting, precision shooting, or long range silhouette? Is your cartridge capable? Is it an old M94 in .30-30 or a .303Br M1, Mk3? Or is it a Barrett M82?
I started reloading with a Lee Loader and a hammer. Made .303Br rounds as good as any $5000 reloading set up. Eventually, I was using a buddy's press to FL resize. He sold me a Challenger for $10. It had a broken toggle link and still loaded .303Br ammo as good as the Lee Loader.
After 30+ years of doing this! I have a number of colours (and shades of colours) on my bench. If a budget is what you have, stay with that budget, be it tight or extravagant. I will say one thing. If Lee is your choice, (and I have nothing bad to say about the Challenger press) spend the extra on a Classic Cast Press. It costs $120 and it is hands down a better press than the much-vaunted RockChucker or the Hornady. I've never used a Co-Ax. None of my reloading mentors had them, so I cannot comment. But I have a RockChucker and have used a Crusher and a LnL. Nothing special about them.
My $.02
True, a Co-Ax will be a slightly more expensive purchase, but to use your analogy, it would not be the difference between a $75 first car and a Range Rover. It would be more like the difference between a $75 dollar first car that might need an alignment and a $100-$150 car that is totally reliable and that someday if you stop driving you will still be able to sell for $75 when you no longer need or want it. (Think long term, not short term.)
Here are a few sample prices (from the same place) for single stage presses (not kits):
Lee Classic Cast Press: $131.03
RCBS Rockchucker Supreme: $191.04
RCBS Summit: $241.49
Redding Big Boss II: $249.01
Forster Co-Ax: $330.74
Hornady Classic LnL Press: $169.99 (This price was from another distributor)
As far as why I recommend it,
from my own experience, I was not getting what I considered to be acceptable results reloading on a Hornady LnL. Maybe I just got one that was slightly out of spec, I'll never know. I was getting variances for instance of ± 5 thou on my COAL on a finished bullet (6.8SPC and .308). I tried changing dies, and that did not significantly improve things. After I moved to the Forster, the variance from bullet to bullet is typically less than ±1 thou.
The spring loaded jaws that the Forster uses to retain the casing does two things. First, it eliminates the need for shell holders. Second, it allows for slight left / right movement of the case. This, combined with the way that the dies are held (which allows for a slight front / back movement of the die) means that the die and the case will always find each other's true center. When seating a bullet, the concentricity will be to extremely high tolerances and this will have a direct influence on your round's accuracy.
By your own admission, you have had
a number of colours (and shades of colours) on my bench.
I am guessing that you have spent a fair bit of money switching through all of those colours (I'm guessing you have spent far more than the $330 that a Forster costs). Imagine how much you would have saved if you started with a press that you didn't feel that you had to keep changing.
True, a Forster Press in not the Holy Grail or Excalibur. It will, however, be a press that you will likely never have (or want) to replace for the foreseeable future, and based on my personal experience, will help you produce far superior reloads (when compared to its competition) for a modest investment.