do you say that it does not matter if the the processor is 32 or 64 bit because if I have a 32-bit OS running on it, 32 bit programs will run just fine on it?
Yes; this is also true for x86-64: You can run 32-bit software on an ISA compatible 64-bit machine. If you've ever had to do that though, it was probably in the context of a 64-bit operating system. This introduces some complications with the 64-bit userspace libraries, which are not necessarily compatible (hence, you probably need two sets of system libs on a 64-bit OS to run 32-bit programs). Note that system libs are I think not a concern for ASM programmers (but I am not one, so I am not positive).
So notice there are sort of two things to consider, the processor ISA and the ISA of the operating system code. There can be a further distinction between the kernel code ISA and the userland system library ISA; you can run a 32-bit userland with a 64-bit kernel.1
The ARM ISA family is, as far as I am aware, intentionally backward compatible. The earliest Pi models have a BCM2835 SoC with an ARM1176JZF-S spec processor. "ARM1176JZF-S" is a microarchitecture: "the way a given instruction set architecture (ISA) is implemented in a particular processor". It implements the ARMv6 ISA. Later models of Pi have processors implementing ARMv7 and ARMv8, meaning they are backward compatible with ARMv6.
Rather than having multiple versions of Raspbian to match the three different ISAs, there's just one that runs on all models using ARMv6 code. Note there are other OS distributions in v7 and v8, but you should regard these as a bit experimental (there may be issues with the kernel) .
Anyway, point being, if you are using Raspbian, there will be a 32-bit ARM native compiler for just about everything. Probably a pretty ideal way to learn assembly!
- Note this backward compatibility between 64 and 32 bit is a trait of the x86 and ARM families, and is not necessary a more general truth.