cost of hosting local classified website for Japanese community

Depending on how big it's going to be, with only a 1000 members who occassionally look at it, you can use a web hosting package for a few bucks per month.
If speed/bandwidth/total data transfer is suffering, you can use a VPS instead. It's a few bucks more. If you use a VPS from the most advanced/biggest provider, you can even upgrade while still in use (others may require a full re-install). It will cost another few bucks per month more.
I don't suspect you'll need more than that.
5 bucks a month = hosting
15 bucks a month = simple VPS
100 bucks a month = powerful VPS

i have already purchased Classima plugin for Wordpress which requires a business plan package from wordpress.com

i checked a business plan at wordpress.com, cost $25 monthly.

does this site come with theme installation capability?

https://www.hostgator.com/promo/wpbeginner1?clickid=1v8wrExKUxyOWwAwUx0Mo3cgUknUc9yAESt90M0&irgwc=1&affpat=1&mpid=11535

any other site, much cheaper hosting?

Cheaper than $2.64/mo???? You did see the feature list included right? (SSL cert, etc etc).

it doesn’t say theme installation capability

Theme installation is INHERENT to ANY Wordpress hoster

Using https://WordPress.com can be very tricky.

Only use https://WordPress.com if you plan on provide your site free forever, so no monetization.

If you plan to every monetize your site, purchase some inexpensive hosting somewhere, maybe InMotion or A2Hosting or a cheap dedicated server from OVH/SoYouStart/KimSufi.