Gotta compare apples to apples, really, as a 401k in an entry-level job (I notice you are pre-med but I don't know your age or work experience or skillset necessarily if you are non-trad) vs. a 401k in a large, generous, profitable corporation could potentially differ greatly. Especially if your skillset is in great demand and rare and you are in an employee's market, a corporation will have to compete for your attention.
IMO a match that starts after 1 year of employment is not competitive compared to a match that starts the first day of the first month after the employment start date, for example. Your delayed match tells me this is an entry-level job with potentially high turnover, or they expect you to jump ship to greener pastures sooner than later. BUT any match is still better than nothing! My last gig was at a formerly Fortune ~400 corporation that had declared bankruptcy and was $1B in debt and was circling the drain, so they made the match 0% then finally 1%. I really miss this one company that matched 7% guaranteed + a discretionary bonus match of up to another 3-4% based on how the company was doing at the end of the year. It's worth shopping around for employers that "treat you well" as all that extra several thousand $$$ here and there early in your career will affect how much your nest egg can grow. Don't settle for "meh" benefits unless you don't have any other options.
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What's the vesting schedule for the match? A competitive vesting schedule is 100% vesting immediately; i.e., what the employer chips in for the match is immediately yours, in which case it would be wise to contribute the maximum 4% to your 401k as soon as you reach the 1 year mark.
It's common, unfortunately, for employers to phase in the vesting; e.g.:
After 1 year - 25% of the employer match is yours
After 2 years - 50% is yours
3 years - 75% is yours
4+ years - 100% is yours
Some may phase it in over 2 years or 5 years or however they design the retirement plan.
A competitive 401k -- like others have said -- will offer "index" mutual funds (looking for the word "index" in the fund name usually helps), which generally offer the lowest expense ratios...preferably below 1%...as close to 0% as possible. I'll be honest: even in entry-level jobs at smaller companies or universities, my best and only option was an S&P 500 Index Fund, and I just threw 100% of my 401k into that single fund and called it a day. I maintain a separate Roth IRA at Vanguard that lets me fill in the gaps so to speak with whatever else I want (e.g. a Total Stock Market Index Fund, Total International Stock Index Fund, etc.).
If you decide to take this job offer, you won't really have to worry about the 401k until almost one year from now, so in the meantime focus on other priorities like emergency fund, Roth IRA, paying off credit card debt if any, etc. And maybe use this time to spend a few hours reading all the great free information from reputable sources on the Web! Knowledge is power, and boy howdy are there lots of people in the banking and finance and investment industry who want to deceive you into making poor money decisions...with a smile.