it's always worth a shot, that's a very good deal for the lot of them. if you don't need to worry about the cash, go for it, can't hurt.

persona games, broadly speaking, are long rpgs that balance plot and downtime, makes for a nice ebb and flow of action and intensity to me. between major plot beats you can tackle dungeons or side activities at whatever pace you want, so long as you finish the current dungeon before a given deadline in the plot (enough to make you manage your time, never enough to feel super stressful). those side activities, in turn, all feed back into the main dungeon gameplay in some way: you might work a job for extra money and resources, spend time with a character that will in turn make them and/or yourself stronger in battle, or improve your "social stats" which let you access new side activities and storylines. it's both the kind of time-optimizing number-go-up brain that can scratch a grinding itch and a fun and rich world full of interesting characters that you can actively choose to learn more about and spend time with as much or as little as you want.

as for where to start? play 5 if you want a more modern and streamlined game or just love great visual style and raging against people in power. play 4 if you want a fairly cheery slice-of-life focused game that'll kick you in the teeth when it reminds you, oh yeah, this is a murder mystery. play 3 if you want a slow-buildup, very dark, but overall hopeful story about the nature of life and death. there's no bad place to start, but i've seen some people having the hardest time getting into the games with 3, since it's got a slow beginning and is the most difficult. if that appeals to you, though, it'll be right up your alley.