Barclaycard Inital isn’t a bad choice. Although slightly harder to get as a first card compared to Aqua, Vanquis or Capital One. Capital One have an eligibility checker that can be pre-approved in some cases. Worth checking.
Just as a side note, your credit score means the square root of !!!!!! all. What matters is the information held on your credit report. The only way to get beneficial information on there is to have credit available, and to use it. Pay off in full and never stretch yourself thin.