Thorlabs sells a 2 mW VCSEL for $30
https://www.thorlabs.de/thorproduct.cfm?partnumber=VCSEL-850 and a 10 mw 904 laser diode for $25:
https://www.thorlabs.de/thorproduct.cfm?partnumber=L904P010.The VCSEL is not single spatial mode, while the 904 laser is, and they have a few other options -- those are just the first two I found.
If they are available at that price from thorlabs new, you can probably get similar things considerably cheaper elsewhere.
Don't underestimate how much power you need. If you use a cheap collimation lens and an aperture to circularize the beam you can easily lose 75% of your light. You get a lot more if you use AR coated lenses and anamorphic prism pairs to circularize the beam, but that is more expensive. In any case, it is always easy to attenuate the light with a filter, it is harder if you don't have quite as much as you want.
Laser diodes can run over a fairly wide range of output power, although the noise and spectral performance will be worse at the bottom range of power. I don't know how much you care about spectral purity or noise. Higher power diodes will also have a larger threshold current, so a 30 mW diode operated at 3 mW will be less efficient than a 3 mW diode. I don't know if you care about this.
So I think a 30 mW laser is probably overkill, but a 5-10 mW one should be perfectly reasonable for generating a 1 mW beam. You can operate it at 25-50% of its rated power and have plenty of room to spare for collimation losses. If you end up with too much power, you can still just put a filter in front. Some polaroid material makes a simple and cheap attenuator.