I have a database with the following structure:
SELECT * FROM users WHERE email = 'email@example.com'
MySQL has two important facilities for improving performance. For your type of query, 500,000 rows or 10,000,000 rows is just not a big deal. Although other technologies such as NOSQL can perform the same actions, applications such as yours typically rely on the ACID properties of databases. A relational database is probably the right solution.
The first facility -- as mentioned elsewhere -- are indexes. In your case:
create index idx_users_email on users(email);
An index will incur a very small amount of overhead for
delete operations. However, with the index, looking up a row should go down to well under 0.1 seconds -- even with concurrent queries.
Depending on other queries you are running other indexes may be appropriate.
The second important capability is partitioning the tables. This is not necessary for a
users table. However, it can be quite useful for transactions and other types of data.