Your cable will do the job you ask of it, but it won't let you have the full 125A down the road
The NEC rated ampacity of a 2/2/2/4 aluminum SE cable when used as a feeder run within an insulated wall is 75A (as the surrounding insulation limits you to the 60°C column in the ampacity chart). However, 75A isn't a standard breaker size, so we round up to an 80A breaker as per 240.4(B). Either way, this is plenty of current available at the subpanel, so enlarging the cable would only be desired if you wished more upgrade room in the future (say -- if you had future plans to convert the basement into an accessory dwelling unit).
If you do want to take that cable back and get something bigger and better, you'll need to get a 2/0-2/0-2/0-1 SER cable to feed the subpanel fully -- this gives you 115A of usable ampacity, and the ability to use a 125A breaker as per 240.4(B). (It also means your minimum bend radius goes up to about 6" due to the cable being fatter.)
As to cable routing...
A 2-2-2-4 SER cable has a minimum bend radius of 5" (5 times the cable's 1" diameter), so getting it to make a U-turn into the top of the panel shouldn't be an issue. You'll need to support it at 4.5' intervals and within 12" of the loadcenter cabinets unless you're fishing the cable through a concealed space (in other words: treat it like fat NM).
Go big or go home!
One mistake many people make when putting panels in is trying to shave pennies by buying a panel with too few spaces in it. While you may only need a handful of breakers now, putting in a large subpanel now is far cheaper than having to rip it out and install the large subpanel later because you needed more circuits. Keep in mind that you can't really make use of double-stuff breakers these days due to AFCI requirements, as the 2017 NEC extends AFCI protection to all dwelling unit circuits (the only exception being a circuit feeding a fire alarm control panel as per NFPA 72).
As a result, the best bet is to buy a big subpanel now. Given that a main lug or convertible panel will suffice (as the main breaker in a subpanel that has one is simply a convenience shutoff for the rest of the panel, save for feeder tap cases you don't have to worry your little head about), I'd recommend a Siemens P3040L1125CU -- it's not terribly expensive, has plenty of spaces as far as subpanels go short of going to 200A bussing, and comes with all the accessories needed -- just mount, pull bonding screw, add breakers, and wire!
TORQUE ALL CONNECTIONS TO SPEC
No mechanic questions the importance of properly torquing the head bolts on a car's engine, and the worst that will happen if you don't is that the engine will break and leave you stranded. Considering that a mis-torqued lug on a panel or breaker can start your house on fire, why question the importance of properly torquing electrical connections? In fact, the 2017 NEC added a requirement to properly torque connection lugs and screws to manufacturer specifications (it's 110.14(D) in the new Code).
So, get an inch-pound torque wrench and/or an inch-pound torque screwdriver and make sure those panel and breaker lugs are torqued to the manufacturer's specifications (they'll be printed on the breaker or the loadcenter's labeling).