Look, getting to Zalissya isn't super complicated but you'll definitely want some essential gear to make it there in one piece. Starting out, swing by Old Mill and grab yourself a Debut Suit from the technician there, it's not fancy but it'll keep you alive through the basic hazards. For weapons, I usually go for the Boomstick you can find up in the windmill stairs - pretty reliable for early game stuff, or if you're feeling adventurous, there's Valik's AKM-74S up in the water tower northwest of town.

You'll absolutely need a gas mask too and I've had good luck with either the Aurora mask (check the backpack stash northeast of Zalissya's rooftops), or the Optician mask if you're near the Cowsheds west of town. Something interesting - always keep medical supplies and repair kits handy, those anomalies don't play nice with your equipment.

Been through here a few times and honestly, the best strategy is just maintaining your gear regularly at technicians, and saving often especially before sketchy areas. Watch out for that trapped Boomstick in Old Mill too, nearly got me the first time! While better gear like the Explorer Suit definitely makes things easier, you can totally make it with just the basics if you're careful and keep everything repaired.