MTB and road front derailleurs have different cable pull, so you have to match the shifter to the front derailleur. 9 speed Shimano MTB derailleurs will index correctly with 9 or 10 speed Shimano road shifters.

You're not going to find a cheaper double road/gravel crank with a 30t low for cheaper than $150. You could use a road triple (50/39/30, typically), or MTB triples are pretty common in 44/32/22.

Were it me for that kind of application I'd probably do a 1x setup with a 42t Sram Apex crankset and a 11-42 cassette. Can be reasonable with a cheaper Sunrace/Microshift 10 speed cassette, Microshift XLE derailleur, and Shimano Deore shifter. This might not have the gearing range you need, but it's worth thinking about.

It can pay to actually do the math on your gearing. I use https://www.sheldonbrown.com/gear-calc.html . For example, with a 38/28 crank wit an 11-34 cassette, you will be going 25 MPH pedaling at 90RPM, which is about what most road cyclists pedal but is a little higher than the average recreational cyclist. 33MPH at 120RPM, which is admittedly a pretty fast spin. Do you care about pedaling down hills or with tailwinds? If not, 38/11 could be plenty of high gear.