Most hand helds are FM voice bands and do not use code in the traditional sense. You can transmit code on this frequency with one but that is generally a specialized aspect of their use. Larger radios using longer wavelengths is the more likely place to use morse code.

That given though, I do think a 2m handheld is a good entry point....just not a very good entry point if CW is your desired communication form. Your first license allows the use of this band, and it generally can introduce you to your local emergency groups.

Ham can be expensive if you buy your gear, but many of the early hams built all their equipment using some fairly lowly items. Some hams still do this...many do it for antennas.

It costs little to study and take the exams, so you need not back burner that. Try and find a ham group locally to assist with your studies and building projects.

Check out the ARRL link I posted above.