Blockchain applications often rely on lightweight clients to access and verify on-chain data efficiently without the need to run a resource-intensive full node. These light clients must maintain robust security to protect the blockchain's integrity for users of applications built upon it, achieving this with minimal resources and without significant latency. Moreover, different applications have varying security needs. This work focuses on addressing these two key requirements in the context of Proof-of-Stake (PoS) blockchains and identifying the fundamental cost-latency trade-offs to achieve tailored, optimal security for each light client. The key security guarantee of PoS blockchains is economic (implied by the "stake"). In this paper we formalize this cryptoeconomic security to light clients, ensuring that the cost of corrupting the data provided to light clients must outweigh the potential profit, thereby economically deterring malicious actors. We further introduce "insured" cryptoeconomic security to light clients, providing unconditional protection via the attribution of adversarial actions and the consequent slashing of stakes. The divisible and fungible nature of stake facilitates programmable security, allowing for customization of the security level and insurance amount according to the specific needs of different applications. We implemented the protocols in less than 1000 lines of Solidity and TypeScript code and evaluated their gas cost, latency, and the computational overhead. For example, for a transaction with value of \$32k, the light client can choose between zero cost with a latency of 5 hours or instant confirmation with an insurance cost of \$7.45. Thus, the client can select the optimal point on the latency-cost trade-off spectrum that best aligns with its needs. Light clients require negligible storage and face minimal computational costs,...