The Deore M5100 crankset retails for well under $100 USD at most online suppliers you'll see googling "Shimano FC-M5100." Combined with a bottom bracket (I, too recommend the SM-MT800. Better sealing and the cups are black in color which will match the M5100 crankset), one can get outfitted for under the figure I mention above.
A chain guide, or simply leaving the front derailleur cage on and manipulating the limit screws so that the chain doesn't rub in the extreme gears is fairly necessary for chain retention in the absence of a clutched rear derailleur. You will need a new 10 speed chain, and I recommend getting a Shimano 10 speed HG-X chain like the CN-HG95. The M5100 crankset is compatible with 10 and 11 speed chains. Compared to a 9 speed chain, the ten speed will be overall narrower, but using it with a 9 speed rear drivetrain is perfectly acceptable and function is normal. It's also good policy, when replacing a crankset or rear cassette with a new one, to start its life with a new chain running on it. Chains always wear out faster than cassettes (about 2-3 per 1) and chainrings (about 6 to 1, though 1x systems tend to be faster wearing than 2x or 3x front drives by virtue of being always in use, so YMMV), and running a worn chain on a new drive train component introduces premature wear to that component. Note that the M5100 is also 11 speed compatible but I do NOT recommend running an 11 speed chain within a 9 speed rear system. The 11s chain is narrower still than a 10s chain compared to a 9 speed chain. The spacing of the cogs of a 9 speed cassette is wider than 10 and 11 speed cassettes. To run a narrow 11 speed chain on a 9 speed cassette risks the chain de-railing and getting jammed between two cogs in the cassette. When this happens under power, the too narrow chain becomes very tightly jammed. This almost always damages the chain to some degree (either the going in or, more often, the force required to remove it) and can mess up deraillurs and cogs as well. The risk of this using a 10s chain in a 9s system is much less.
Lastly, depending on how you intend to use the bike, you will be losing a great deal of range, especially at the top end. The max chainring size of the M5100 is 32 teeth. While they do make wider range 9 speed cassettes like 11-42 teeth (SunRace), typical MTB 9 speed cassettes have a range of 11-34 teeth. A typical 9s crankset would have a top gear ratio of 42/11, or 3.82. This will translate to a speed of 26mph at 90rpm on a 26er. With a 1x 32t front your 32/11 ratio is 2.90 and speed at 90rpm on a 26er is 20mph. This may or may not bother you, but in any case, your max speed will be reduced and you may find you're spinning out often enough where you ride that is becomes bothersome. You may be able to purchase, fit and use a larger, third party's chainring and get up to 34 or 36 teeth but that is contrary to your desire to not spend a great deal of money on this conversion, compatibility must be determined.
So there's a lot of info for your proposed upgrade. Some positives and some drawbacks. Overall, my feeling is that your choice of crankset is reasonable as far as price and that it is an upgrade for sure compared to the SunTour. However, the unwillingness to pair the Deore crankset with other components more suitable will minimize the potential increase in performance. You will reduce weight significantly by losing the cartridge bottom bracket, some chainrings and inferior SunTour crankset and at least the shifter and cabling of the front derailleur, so that is something.