BoardGameGeek is the place to read up on games before buying them.
On the 'without spending money' front, depending on the city where you live, there often are board game cafes where you can go to rent games and play over there.
More economical if you are playing the game once or want to try out different games. Also very good if you struggle with learning rules from the rulebook.
One thing that would help if you could figure out the types of games you and your group might enjoy — or the type of group you and your friends are.
If you think you’d enjoy deeper strategy games, start with some of the popular games in the “strategy” category on BGG, looking for light to medium weight (1.5-2.5) to start out, working your way up the scale (to 3.0, 3.5, and 4.0).
If you’re more into the social/party type games (those are always more fun in larger groups), look at the party category. I particularly enjoy social deduction games in the right group, and those are usually big hits with older kids / younger adults (though I still enjoy social deduction games and I’m quite beyond “younger adult”). :)
One good example is One Night Ultimate Werewolf.
One tip: if you’re interested in trying out some strategy games that are a bit out of your price range, check out boardgameoracle.com and add price alerts on a few games you have your eye on. Many great board game sites run good deals (gamenerdz.com is one of my favorites), so you can often get good deals on games if you’re patient.
If you ever get to the point where you’re looking for something with a bit more depth, and are ok spending money, but you want the money to go a long way, Age of Steam is one of the best bangs for your buck.
It’s basically a system that has a library of probably close to 200 maps, where each map can change the game quite drastically, by tweaking several rules, in addition to a different map of course.
It’s currently my #1 game, and you could repeat plays with it without it getting old, assuming others enjoy the mechanics of game (route building, auction/bidding, tight economy).
It's called "So Clover!" and it's a word association themed game where each person gets four pairs of words, you write a one word clue for each pair, and then the rest of the group has to work backwards to figure out the original orientation of your cards (the cards themselves each have four words as well)
For a nice entry game for a group setting, I recommend Carcassonne. It has a simple and engaging basic gameplay with a surprising amount of depth, that can easily be scaled up and down in complexity depending on your group's preference and experience level by simply adding more pieces/mechanics.
Our oldest child is now capable of the base game, and I can still make it interesting for me by going for secondary objectives, such as filling difficult gaps ;-)
When my girlfriend and I play, we sometimes give unofficial bonus points as compensation for suboptimal plays that fill out unseemly gaps that would otherwise stay open. Makes for a nice, aesthetic endstate board without handwringing over your score :b
The beauty is that it visually looks really complex and advanced, but the gameplay isn't really that much complex more than wingspan.
Over the years I bought the 'prelude' expansion which speeds up the beginning. (Highly recommend)
And then once you've played it more than 10-15 times, the Hellas& Elysium adds more maps for variety.
If not, maybe there's an adjacent group that might also be willing to entertain board games, or it's a group you could found. My college had a gaming, anime, and chess group which anchored my social experience.
Pandemic. Ticket to Ride.
Modern classics, great fun, easy to get into.
For meatier games I really like Scythe: https://boardgamegeek.com/boardgame/169786/scythe
I really recommend trying a trick-taking game! Skull King, Fox in the Forest, Tichu. Easy to learn, impossible to master.
Another quick, low-complexity game that is easy to teach & pretty good fun is Century: Spice Road [2]
Chinatown [3] (re-themed as Waterfall Park [3b] ) is a simple highly interactive game that is basically 100% negotiations between players who are trying to make real estate deals with each other. Can be played in 90 minutes, including rules explanation, plays up to 5. For a more complex asymmetric game that's more focused on engine building, with a healthy dose of negotiation, check out Sidereal Confluence [4].
For more complex games that take a bit longer to play to teach and play, that are largely focused on players doing their own thing ("multiplayer solitaire"), building their engines without much negative player interaction, check out Ark Nova [5] or Terraforming Mars [6]. These might take 3-4 hours or so to finish, provided there's an experienced player to teach everyone the rules.
For another moderately complex strategy game with a little more player interaction, check out Brass: Birmingham [7]. Takes around 4.5 hours to finish a 4 player game, including the rules explanation. If you have a group that enjoys complex strategy games and wants something with spikier negative player interactions, where one player's actions can completely wreck another player's plans, check out Barrage [8].
This probably doesn't help "without spending much money"! One trick is to find or create a regular board gaming group where everyone brings along different games. That way if, everyone buys a new game or two every year there's a lot of variety without everyone needing to buy heaps of games.
[1] https://boardgamegeek.com/boardgame/364073/splendor-duel
[2] https://boardgamegeek.com/boardgame/209685/century-spice-roa...
[3] https://boardgamegeek.com/boardgame/47/chinatown
[3b] https://boardgamegeek.com/boardgame/396618/waterfall-park
[4] https://boardgamegeek.com/boardgame/202426/sidereal-confluen...
[5] https://boardgamegeek.com/boardgame/342942/ark-nova
[6] https://boardgamegeek.com/boardgame/167791/terraforming-mars
[7] https://boardgamegeek.com/boardgame/224517/brass-birmingham
So make amazing suggestions in this list, including two of my favorites: Terraforming Mars and Brass Birmingham.
Just chiming an opinion that Brass Birmingham is high on the complexity scale for beginner board gamers. Or more specifically, high on a frustration scale because there are so many placement restrictions that there are often only 1-2 legal moves to play and figuring out what they are is quite a challenge for people playing the first time. (From experience that we as well as several others we know had on their respective first times)
That said, I absolutely love the game!
Also, some of those legal moves will set up a board state that the player taking a turn immediately after you can exploit for a lot more benefit than you got, so not only are the legal builds hard to identify for new players, half of those legal moves are also traps! If new players aren't comfortable learning the hard way, the player who is teaching the game can always call these out, explain what is going to happen & give people the opportunity to redo their move.
An alternative strategy game that is less complex than Brass is Friedemann Friese's classic Power Grid (2004) [1]. It has some of the same elements (network expansion, building stuff to make money) and parts of it are highly interactive (auctions!) but it is less complex and doesn't feature so many negative player interactions. The main down side of Power Grid is that some of the "admin" rules are pretty fiddly, but provided there is an experienced player to teach the game & be responsible for the admin, players who are learning don't need to care about the details.