Reddit mentions of TRP RRL Alloy Brake Lever Set, Black - RRL AL-B

First of all, I think that's a pretty nice frame. Double butted Tange steel tubing means it should be decently light and strong. Was a middle/higher end bike back in the day. Definitely keep it...it's worth fixing up.

Don't know anything about those tires, but the rest of the purchase looks fine. 28mm tires will "probably" fit, so good luck with that; bikes from that era had a bit more clearance.

You may also want to check if any of the other wear parts need replacement. This is usually the case if the bike sat unused for years: brake cables and housing; derailleur cable and housing; brake pads. After a decade, cable and housing often get gummed up and pads get hard/dry. Getting good brake pads like Kool Stop will make a huge improvement.

With the tires off, scrub the rim braking surface with a brillo pad or something similar, using vodka or rubbing alcohol, whichever is more available.

Check for chain wear with a chain checker (a $5 tool) or measuring with a ruler (google it). If the chain wear is fine and it isn't horrifically corroded with rust, it'll be fine even after 10+ years.

For commuting, I suggest a nice set of generic pedals that are wide, have good bearings, and have good grip. I've had good luck with various Chinese pedals, like this set: https://www.amazon.com/gp/product/B07DHHQQHG/ref=ppx_yo_dt_b_search_asin_image?ie=UTF8&psc=1

You didn't post a pic of the actual bike. But if it's got the original levers, the single best thing you can do is to upgrade with modern brake levers which are substantially more ergonomic:

https://www.amazon.com/Tektro-RL340-Brake-Lever-Black/dp/B01173986A/ref=sr_1_9?keywords=brake+levers&qid=1565320277&s=sporting-goods&sr=1-9

https://www.amazon.com/TRP-Alloy-Brake-Lever-Black/dp/B007DCFKE4/ref=sr_1_18?keywords=brake+levers+cane+creek&qid=1565320183&s=sporting-goods&sr=1-18

Yes, there may or may not be other things to overhaul, like bearings and such. But save that for later.