Non-fungible tokens (NFTs), attracting interest from a variety of audiences including collectors and traders, saw transactions exceeding ${\$}$50 billion in 2022. The inherent features of blockchain technology-distributed, immutable, and transparent-make it an ideal platform for verifying ownership of digital assets. Despite these advantages, the high computational and transaction costs of networks, which utilizes proof of work pose significant challenges. To overcome these, alternative public blockchains have been developed, each offering unique benefits for NFT marketplaces. Choosing the right blockchain platform is crucial but complex. In our study, we introduce a prototype NFT marketplace optimized for scalability and efficiency, capable of rapidly handling a large volume of NFT transactions. We also conducted a comparative analysis of various public blockchains to identify the most cost-effective and reliable options for NFT exchanges. Further, we developed two predictive models to enhance decision-making around transaction fees and error management, thus improving cost-efficiency and reliability. We also propose a self-adaptive mechanism that allows for dynamic switching between blockchain platforms, enhancing the flexibility, and overall performance of the marketplace. Our contributions are integrated into IntelliChain, a self-adaptive framework designed to predict optimal transaction fees, reduce errors, and adapt to changing conditions like network stability and fee structures, bolstering efficiency, and reliability.