Beginner question

Hi ppshil.  Many fine choices have been mentioned.  The best one for you will depend on your budget and shaving preferences.  Other things being equal (OTBE), do you prefer lighter or heavier razors, or does weight not matter much for you?  Again OTBE do you prefer very efficient razors or very smooth ones?  Here are a few considerations which, despite being peppered with my opinions, you may still find useful.

• As time goes on, I believe more and more in my hunch that for every shaver, there is probably a vintage Schick that shaves as well for that shaver as any razor ever made - vintage or modern.  Vintage Schicks (aka Eversharp) tend to be cheap, and they use the rigid, reasonably priced, nimble injector format blades.  On the downside, not every vintage Schick is a jewel, and those that are reflect several decades of production and design tweaks, during which some razors were more efficient, and others were milder.  You may need to experiment to find your own sweet spot.  The conventional wisdom is that older Schicks are more efficient/aggressive.  Here are two sites, Schick History and Chronology, that will help you understand Schick related terminology commonly encountered on forums and sites like ebay.
  
• There are two modern Schick formatted razors that come to mind, the Supply, which has older and newer versions, and the Asylum Injector.  I have the older Supply version and the mild, mid, and efficient plates.  I think a lot of this razor, but as time goes on and my tastes have changed, I do find the older Supply model on the heavy, bulky side, and not especially easy to hold side.  The Asylum Injector (which does not actually inject, but which does use injector blades) is recently released (July 1, 2022).  This razor is on the pricier side, but the initial buzz is positive. 
  
• I personally divide Artist Club (AC) safety razors into two groups: the Blackland Vector (in stainless or titanium), and everything else.  The Vector is painfully pricey, but there is abundant love for it for very good reasons.  The Vector is an elegant, well thought out design from a well respected vendor.  Among other things, it is well balanced, reliably manufactured, and more nimble than any other AC safety razor I have used.  There are, however, other upscale AC razors I have not used.  Nevertheless, my personal opinion:  If money is no object, start here.  There may be a better, cheaper razor with your name on it out there, but the thrill of the hunt will wear off as you bleed along the way.  If you want your best shot at a razor you will own for a lifetime and at fun from day one, start with a Vector. 
  
• The Hawk, which has been mentioned, is a very fine razor from another well respected vendor.  The stainless Hawk comes in standard (V3), more aggressive (V3A), and open comb versions.  Like many razors offered from Italian Barber, the Hawk is reliably made and an excellent value.
  
• I personally agree with those who feel the OneBlade has been overly criticized, but even so, I would not recommend it, at least not as a first choice.  If I were going to buy a one blade, I would look for a used version 1, which allows despined GEMS to be inserted without further modification.  The current version (V2 I believe) comes in Core, Hybrid, and Genesis.  All of these V2 versions will not work with unmodified GEM blades.  I own a V2 Genesis, and I occasionally use (and enjoy) it with either the pricey Feather FHS-10 blades or with modified GEM blades.  If I were buying today, the Hybrid is the only model I would consider.  The Hybrid has the metal head but lacks the Genesis price tag.  The Core does not have the metal head, and some users have managed to damage it while inserting the blade.
  

That's all I can think of at the moment.  Good luck whichever way you go.

 

Very concise and organized presentation, Mike HighSpeed. Well Done, my man! Regarding the core, I now feeling pretty well-versed in the options. A good bit of research all around! I am bookmarking this one!

Remember that single edge razor blades are thicker than double edge blades. That means SE blades do not curve within the head of the razor. While DE razors are normally designed to be used with the head somewhere around a 45 degree angle, SE razors are designed to be used such that the cap of the razor is flat against the face. This allows the SE blade to cut at a very shallow angle. Pivoting head cartridge razors operate using this same principle.

Yes and the biggest issue with carts is the angle they use. I've found that angle cuts hair in such a way it likes to cause ingrown hairs aka shave pimples. If you changed the angle to closely match SE razors they would for all practical purposes shave the same. With that said the Schick injector razors in my opinion are the most cart like of a shave but doesn't suck like a cart shave.

The original single blade disposable and cartridge razors performed in a manner quite similar to the injector SE razors. The multiblade cartridges, especially those with 4 to 6 blades are more likely to experience the issues you note with ingrown hairs. More does not always mean better. IMHO, the three blade cartridges like Gillette Mach3, Schick Extreme 3 and BIC Hybrid 3 might be the sweet spot for cartridge razors. However, I still prefer using straight razors, SE razors and DE razors rather than multiblade cartridges.

I found a Above the tie SE1 aluminum for $60 on BST. Definitely worth the price IMO

I would probably try a Razorock Hawk. ...

I have what I think is a Version 1 of the RR Hawk, and I'm not that crazy about it. It feels too rough or too aggressive to me.
I've only ever tried it with "KAI Captain Titan Mild" blades though. Any suggestions for a different blade that I might prefer?

I would probably try a Razorock Hawk. ...

I have what I think is a Version 1 of the RR Hawk, and I'm not that crazy about it. It feels too rough or too aggressive to me.
I've only ever tried it with "KAI Captain Titan Mild" blades though. Any suggestions for a different blade that I might prefer?

I don't think I have ever seen the V1 up close. I started with the V2 so this suggestion may be less helpful. I found the Schick Proline blades to be a nice balance on smoothness and efficiency in the V2 and maybe a bit less so in the V3.

I do like the KAI Captain Mild (unguarded) in the Vector. By chance are you using the guarded version of the KAI Captain Mild? I find the guarded versions can feel less smooth. Although some really enjoy guarded blades in general. Another one to consider might be the Feather Soft Guard. They are definitely milder and for a guarded blade they are pretty smooth, at least to me.
Edit: Probably good to check if the Soft Guard is compatible with a V1

I don't think I have ever seen the V1 up close. I started with the V2 so this suggestion may be less helpful. I found the Schick Proline blades to be a nice balance on smoothness and efficiency in the V2 and maybe a bit less so in the V3.

Now that I've read the description at Italian Barber more closely, it appears that my Hawk is actually a V2. They make references to such "new" features as three lather slots in the guard, the curved top, and a handle that you can unscrew the knob from.

I do like the KAI Captain Mild (unguarded) in the Vector. By chance are you using the guarded version of the KAI Captain Mild? I find the guarded versions can feel less smooth. Although some really enjoy guarded blades in general. Another one to consider might be the Feather Soft Guard. They are definitely milder and for a guarded blade they are pretty smooth, at least to me. 
Edit: Probably good to check if the Soft Guard is compatible with a V1

The blade dispenser look like this:

Nothing about a "guard".

I'll have to check out the ones you mentioned. The "SoftGuard" type must be the pink one in this chart.

I must confess that I'm not clear on the distinction between "Thorough shaving" and "Relaxation". That's a new parameter to me.

Ooh - yet another chart:

John Rose, the guarded blade packaging looks like this:
  


IME they can make a big, positive difference under some circumstances.  

Hey John Rose I found ANOTHER chart!! 


I swiped this from Amazon.