What is a roguelike here, and which one should you start with?
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A roguelike is a run: you start fresh, choose an upgrade or a card after each win, and what you built lasts until the run ends. All five here are single-player and free to play in your browser. Start with 
Voidwake Space Shooter for reflexes, Oxbow Deckbuilder for cards, or 
Bastide Tactics for grid tactics.
What do you choose along the way?
Shardfall Brick Breaker offers one of three upgrades from eleven after every wave, and sends a moving boss every fifth wave. There is no set number of waves, so a run lasts as long as you do.
Voidwake Space Shooter runs a 50-level campaign in five sectors with an upgrade pick after every level. Cinderhold Survivor runs twelve minutes per stage across ash, bog, snow, crypt and fire, each with its own boss, and lets you carry six weapons and six passives, which evolve when paired.
Bastide Tactics holds a valley across four regions, and lets you choose between two fields before each battle. Oxbow Deckbuilder gives you a card after each win and a boss at the end of each of three acts.
Does anything carry over between runs?
In some of them. Cinderhold Survivor turns gold from every run, won or lost, into permanent ranks in the camp shop. Bastide Tactics opens more wardens with renown, and Oxbow Deckbuilder unlocks its Undertow hard mode when you win a run once.
Frequently asked questions
Can I play a roguelike with a friend?
No, all five are single-player. For a friend, the Online games with friends list collects the games with a room link.
Is there a daily run?
Yes, in all five. Everyone gets the same layout or river that day, so scores are comparable, and it resets at 00:00 UTC.
How long does one run take?
It depends. 
Cinderhold Survivor is twelve minutes a stage. 
Shardfall Brick Breaker ends when you lose, and 
Oxbow Deckbuilder takes three acts to finish.