SPS , ADL, BDL are all Remington rifles in different grades. SPS is relatively new low grade (cheap) with plastic stock and very few frills finishing. The ADL is an older designation of their low end bolt rifle, plain wood stock or plastic no extras. The BDL is a more refined finished rifle with a floor plate, cut checkering typically in a a decent piece of wood or possibly a fiberglass stock. They all use the same basic bolt parts with different degrees of finish.

Talley LWs are in reference to Talley 'lightweight scope ring/mounts'.

To tune a trigger is to hone the sear surfaces to get a clean break and a desired pull weight. Typically this work is done by a gunsmith and often instead of tuning a trigger you can replace it with a aftermarket of better quality than the factory.

An "AI" is a chambering that has been re-cut to enlarge the riflechamber.
Example 22-250 or 22-250 AI. The chamber of the rifle is cut larger allowing the standard round case to fire in it but after firing the case takes on a larger, less tapered, sharper shouldered configuration allowing for slightly more powder, thus more bullet speed. The AI will require new dies and new data.

There are many after market triggers and barrels. You will find nearly all are superior to factory barrels and pricing runs the distance. I like Shilen barrels but others have their preferences. Are far as triggers a Jewel is good so is a Riflebasics.