I made a mistake. I purchased DeLonghi La Specialista, and I am not happy with the internal grinder. I just cannot dial it in. I need to always overdose and to grind to the finest settings. Not to mention it has pressurized baskets only. I need to purchase a separate grinder.

Now, the QUESTION: I want to purchase a 51mm portafilter and an IMS (or any good one) 51mm single wall basket for it. Will any 51mm basket+portafilter fit my Delonghu La Specialista? Any recommendations, please?

Portafilters are usually specific to brands which is frustrating.
You should be able to get a single wall basket that will fit your existing portafilter. That is where I would start. A lot of portafilters that are designed for double walled baskets also have a plastic distribution plate that you can remove to fit a deeper basket. Once you understand the diameter of basket, then you must make sure the portafilter is deep enough for the basket.
Single wall is a definite improvement, but the biggest improvement you can make is a decent grinder.