Help choosing an outbuilding sub-panel
Lots and lots and lots of spaces.
Electricity works for us. It does our bidding.  Running out of spaces is a huge, project-killing problem.  And spaces are dirt cheap when you buy it (rather more expensive after the fact)... so we earnestly advise gross overkill on panel spaces.
So when you said &quot;150A panel like this one&quot; I thought &quot;30 space panel for a shed?  Now you're talking!&quot;
Seriously.  30 spaces is not too many.
So yeah, if you want to get a similar subpanel, go for it.  Although that one is a classic &quot;CH&quot; panel, I have 2 myself and they are my brand of choice.  They are now wider because of a rule change on wire bending radius.  14.25&quot; so they fit between joists.
If you're thinking &quot;I'll free up THAT panel when I upgrade my panel&quot; I would not do that.  I would leave this panel where it is and put a new 200A CH panel right next to it, then have that feed this existing panel.  Way less work lol.
Main breaker size in a subpanel
Subpanels don't need main breakers at all.  What they need is disconnect switches if they are in outbuildings (no breezeway between them).
Actual disconnect switches can get pretty expensive, and just the way they price service panels, it's cheaper to buy a &quot;main breaker&quot; panel and completely ignore the number on the breaker handle.
So yeah, a 150A main breaker panel will work for ANY feeder size, though a feeder larger than 150A would be wasted.
The feeder MUST be fused
You mentioned 150A feeder to the subpanel.  However you can't &quot;tee&quot; off the un-fused, always-energized feed coming off your meter and carry it to the subpanel. The run to the subpanel must be protected by a breaker.  And here's the rubaw: the largest branch circuit breaker in the CH line is 125A.
To go off on my tangent about a panel upgrade, one option is to replace the meter pan with a &quot;meter-main&quot;.  It contains both meter and main breaker (some even have a micro-panel with 8 spaces that is perfect for feeding outbuildings).  At that point the wires coming off the meter are fused, and you could &quot;tee&quot; off them at your leisure.  It's a complicated job that requires permit/inspection, but the scope of work is small.
So the feeder wire must be behind a breaker, and the breaker decides wire size.  Since you're in conduit, we're talking THWN/XHHW individual wires, and those are allowed to run hotter than UF/NM cable, so amps may not be what you expect.

30A -- #10 copper wire
50A -- #8 copper wire or #6 aluminum
65A using 70A breaker -- #6 copper or #4 aluminum
100A -- #1 aluminum
120A using 125A breaker (largest 2-space breaker) -- 1/0 aluminum
Full 150A -- 2/0 aluminum for you

You can actually provision full 150A on 2/0 wire (135A normally), because of Rule 310.15(B)(7) which says &quot;no feeder needs to be larger than 83% of the service size&quot;, that's 124.5A in your case.  Services &quot;round down&quot; on breaker size, feeders &quot;round up&quot; as above.
#6 or larger is where you start thinking about aluminum wire.  Much above that, aluminum is the wiser choice. The lore about &quot;dangerous aluminum&quot; never applied to large feeder like this.
Grounds must be #10 for up to 60A, #8Cu/#6Al for 61-100A, and #6Cu/#4Al for 101-200A.  That's decided by wire capacity not breaker size! (if conductors are upsized e.g. for voltage drop, grounds must be too).
You aren't going far enough for voltage drop to matter at 240V, I don't even crunch the numbers until 180'. However I also like to recalculate for a single large 120V load, and on smaller feeders (#12-#10) that can become an issue. Even so, you're just on the cusp; I don't even bother crunching the numbers on that until 90'.
Your questions
Is 150A overkill?  Yes, until the day you're at the Tesla dealer who asks &quot;do you want the slow charger or the fast charger?&quot;  Prior to the existence of EVSEs, most people had little chance to use that much.  But there's always another gadget, and always will be.
Is my panel big enough? Always.  Panel capacity isn't decided by subpanels or spaces, it's decided by load calculations based on the loads of the house.
How do I choose the best size sub?  Spaces: PLENTY.  Amps: Any size, at least enough to exploit whatever feeder you're willing to pay for.
Remember you need 6&quot; of cover over top of the conduit, not a 6&quot; trench.  Also must be 12&quot; under vehicle drives.