I want to start hosting a regular boardGames

Task prompt

I want to start hosting a regular board game night for three to five friends, but I own no modern games and my group has mixed experience. Use Wikipedia's Eurogame reference, its board game reference, and its tabletop game reference to explain what makes a modern gateway game work for a mixed group, like play time, player count, and simple rules. Price three different gateway games suitable for 3 to 5 players on Amazon, keeping the total under $120 if the available listings allow it, and tell me which one to learn first. Finish with a written starter plan that lists the three games with specs and prices, key concepts for teaching, a learn-first recommendation, and a simple hosting checklist.