Another reason Hearthstone was so frustrating. All the legendary cards were locked behind astronomical paywalls.
It's been a while since I played, but does look like for IP reasons you'll need to actually download the cards separately from the actual program. I'm not sure where to do this, but I'd imagine someone on this subreddit or on their dedicated Cockatrice server can help you https://www.reddit.com/r/Cockatrice/
If you want to play in the computer, there are several free and open source implementations. I don't have any great recommendation, but I'll just point out that I sometimes play around with XMage (http://xmage.de/) when I feel like whacking around the AI a bit. Too bad it is so unstable and crashes a lot :(
It's modeled after real time strategy games (Warcraft 3 especially), and was designed by David Sirlin. Sirlin writes about game design, and I've really enjoyed his commentary on competitive systems. He did the rebalancing for Super Street Fighter 2 HD Remix, and the changes he made are discussed in a series of articles here: http://www.sirlin.net/articles/sf
You can various other articles he's written by clicking around that site.
You can even do play by post, since you only make decisions on your turn. You have to trust the other person to shuffle, but it works
But if you like the base game, you can probably snag someone's collection on the cheap, on Craigslist.
I'd bet the overwhelming majority of Dominion games are not just using the base set, but the "recommended first play" card selection.
Put the 'proxy' cards in a sleeve with a regular card behind it.
Takes time and effort, but if you play one night a week or so it ends up more fun because you never know what someone is going to bring.
There is also Apprentice, kind of like MtG online but with barebones interface, that allows you to play against other people.
Then, you simply slip your rectangles of printer paper into a card sleave with a real Magic card (usually some card you don't care about such as a basic land) and tada, you've got whatever cards you want and all it cost was ink and time time.
Interface is amazingly complicated though, since it has to model all of MtG.
MtGO: old official version, you can buy and sell singles for similar costs to paper
Cockatrice: Old unofficial free version. leaves a lot of rule/effect enforcement up to players manually.
Duels: "new" official version, never implemented complete rulesets, abandoned by devs 2 years ago, leaving collectors who paid good money SOL
Arena: new official version, but with hearthstone model of only RNG card purchases, no singles or resales.
Personally, after putting close to 4 figures into MtGO, then hundreds into duels for nothing (on top of the fortune I've spent on paper), the price fatigue has ruined arena for me, and I don't give them any money.
(to ruin the joke: this is where the famed bitcoin exchange MtGOX came from. It was an exchange for MTG Online that was repurposed into a bitcoin exchange... with that kind of flawless pedigree who could have ever foreseen problems coming down the road? /s)
But for real, the target demographics (nerds who want to speculate and also feel like they're doing something cool) made it the great fit it was.. especially when magic speculators themselves needed a better vehicle for peer-to-peer value exchange.