I would agree with Mamya regarding Azed. One particular advantage of Azed over most barred puzzles is that it is always set by the same person, so you can relatively quickly get used to the setter's style. Also the puzzles are largely 'plain' (unthemed), which makes for an easier transition from blocked puzzles, while the clues are well-written, fair and witty
There is no fundamental difference between barred and blocked puzzles, although you are likely to encounter a higher proportion of obscure solutions in barred puzzles. To balance out the increased difficulty that this creates, less unchecked letters are allowed in the entries and the wordplays in the clues are required to be grammatically sound.
Having Chambers dictionary (either paper or electronic) to hand will make life a great deal easier when it comes to the obscurities. Setters are normally expected to indicate obsolete, dialect, regional etc words (by the use of qualifiers such as 'old', 'local, 'in Glasgow') - Azed always does this, but it's not a hard and fast rule for all barred puzzles.
There is a large archive of Azed puzzles on the Guardian web site (https://www.theguardian.com/crosswords/series/azed) and a blog for each puzzle is published on the fifteensquared site (http://www.fifteensquared.net/category/azed/), explaining the solutions and facilitating further discussion.
Good luck!