If I were you, I would ask myself two things before deciding on the volume of the tank:
How much space do I have, max? (and) Will she want more than just the betta?
If you have enough room for a 5g+, go for it! The more water, the better. Easier care, easier medication, easier hardware, easier overall, and after all that 'easy', happy betta.
If she will want more than just the betta (we've all been there), think of her future options.
A 5g will leave very, very few options. Generally speaking (I do mean general), she'll be left with African Dwarf Frogs and Apple Snails between 2 and 5 US gallons of space.
I encourage you to get a heater. Now, if her home is warmish, it'll rarely turn on. On the plus side, when she experiences some sort of cold spell, it WILL, and the betta will not die. In tanks less than 5g, you generally are not able to get a heater. Heaters are only really reliable in volumes 2g and above. Between 2 and 5g, you can't control the temperature... not really. Commercially available heaters only heat a few degrees above room temperature, for that range. 5g+, you can get a dialed heater, which turns on and maintains (theoretically) the water temp when it dips too low.
A filter is optional at 5g, and generally unnecessary 5g -.
Basically, at 5g -, you make it pretty. At that point, it is your responsiblity (not the heater, not the filter, nothing) to maintain water params.
A betta in a tank that is 5g- is an actual responsibility. If you suspect that she might skip a day or two, consider a larger volume, your future pet will thank you.