Also, 3.5A absolute max mosfet dc current doesn't seem to be enough for a 2A motor, at start you will have peaks higher than that, unless you plan to cap the current with a resistor or something
I wasn't planning on using anything other than the MOSFET. What's a good rule of thumb in terms of the max current for the MOSFET to handle a 2A DC motor? These MOSFETs are cheap, so I have no problem going to a higher current.
The max current is basically marketing nonsense. To calculate if a MOSFET is suitable, you need to be focussing more on working out if you meet the max power and max junction temperature specifications.
The idealistic approach to selecting a MOSFET is to take all available MOSFET, filter out the ones that will blow up (i.e., exceed max current, power OR temperature), calculate how hot the remaining ones will get (using Rds(on), not max current ratings), and choose a compromise between that factor and cost. Obviously I'm not suggesting you do this exhaustively for all MOSFETs; I only point this out to make the point that asking for a max current rule of thumb here is really missing the point.
In particular, since you're not doing PWM, you can tolerate a fairly high gate capacitance, so if I went through my selection process, I'd probably end up using any cheap old MOSFET "rated" for 50-100A. IRFZ44N is something I have lying in my MOSFET drawer here. Not because I targeted 50-100A, but because I was looking for low Rds(on) (which translates to lower wasted heat via the formula P=I^2 R).
Edit: Amongst SOT-23's at Digikey, Si2342DS is the best available option. 17 milliohm Rds(on) at 4.5V, and a nominal rating of 6A. Not sure if that's sufficient or not, depends on the current profile of the motor at startup.