Re: Blackboard: Yes, it works perfectly fine this purpose. I use it for weekly multiple-choice quizzes in all my classes and find that it benefits my class management a lot. It's automatically and instantaneously graded, provides immediate feedback to students, a 24/7 grade center that students can check on at any time, and copious statistical reporting on the back end which I use to drive future updates in all of my classes. There are lots of options now that you may want to investigate. A few pointers:
One: How you make Blackboard tests in the first place is a bit of a question; I find the web interface a bit slow and inelegant. Personally, I find it more efficient to make my quizzes locally in Pearson TestGen, and then export them to Blackboard as a separate step. TestGen looks like this:

Two: While the most familiar use-case is for multiple-choice questions, Blackboard has many other formats of questions you can use. Just one example: For quantitative questions, you can require numerical input that gets scored as correct if it matches a certain number within a certain tolerance ("Calculated Numeric"). You can even include variable questions, so different students have different questions, with a formula under the hood that determines the correct answer ("Calculated Formula"). Limitation: The answer must be a decimal-notation number; fractions and algebraic expressions cannot be constructed/graded automatically in this way. (Also, my Pearson TestGen process doesn't work for more than simple multiple-choice items.) List from the Blackboard interface:

Three: The back-end statistics are so fascinating that I find some amount of risk in being a bit personally addicted to checking them on a daily basis. You can also export all of the individual responses to an item and run statistical tests (in, say, a spreadsheet or SPSS) looking for what important factors correlate with entry diagnostics, final exam scores, etc. Here are some samples of reports from within Blackboard:

Finally, if you don't want automatic grading of tests, then that's supported as well (e.g., for essay, coding, or other subjective questions); tests come in and then the instructor gives grades and feedback via the interface later. Also there are "assignments" in which students can upload documents and then the instructor grades them likewise (including possibly use of a "rubric" which allows grading by selecting from among several radio-button options).