When betting on a player's first-round match in a non-Grand Slam tournament, key factors to consider include the players' current form and recent performance, head-to-head records, surface suitability (as different players excel on different surfaces), odds provided by bookmakers reflecting market sentiment, weather conditions that could affect play, travel and fatigue factors if one player has recently played in another tournament, and any potential injuries or fitness concerns. Additionally, assess the motivation levels of the players, as some may prioritize smaller tournaments differently, and consider the historical performance of players in similar tournament settings.