Having done this, especially with the Psalms after completing the entire syllabus outlined in Weingreen, I have to say it really makes learning Hebrew more meaningful. Try this!
The Psalms is a great book to start with, especially since most of us already know the contents in English. Psalms are poetry in nature; therefore, they are short verses and packed with meaning.
You should go through the Psalms verse by verse. There are verses in it that you are familiar with that you can mediate on throughout the day. I do this all the time. Whether driving or cooking, or while having my shower, I occupy my idle mind with the Psalms in Hebrew.
My initial plan was to memorise some of the favourite Psalms in Hebrew. However, I think the more important step is to first meditate on the meaning first. While meditating on the Psalms, I realise that I was able to review my Hebrew grammar, something which I agree can be too "mechanical" while going through Level 1 and 2 Biblical Hebrew.
While the grammar and vocabulary are necessary in the learning of any language, we have to supplement it with the syntax and the way words are used to produce a specific effect.
This will not only help you review your understanding of concepts such as cohortative, imperative and jussive (which you learnt in Hebrew Level 1), when you see how these words function within the context of a given situation; meditating on God's Word in Hebrew will also help unleash a new zest in learning the language.
You will also how beautiful and precise the language is because the Psalms are poetic in nature. Those of you who did English literature (I did not) will be able to understand this better why you were told to read William Shakespeare. What a feeling when you begin to build your confidence in handling the language the way it is used!
If you follow this piece of advice, your feeling that Hebrew Grammar (same with English Grammar) is too 'mechanical' and 'dry' will be gone. The new insights that you have gained through the learning of Biblical Hebrew at Levels 1 and 2 seminary level will give new meanings to the text that you are reading.
For those who know how to sing, it is a also good to sing some songs in Hebrew after going through the lyrics in Hebrew. Go back to those days when you were in nursery school where you learnt the nursery rhyme by hard and sing along with your teachers.
Those of you who are able to download "Daily Dose of Hebrew" on your mobile phone will find the grammar being explained as the verses are parsed, glossed and given the English translation. For example, this morning (Oct 1), the gentleman parsed the Pe-Yod (I-Yod) in Psalm 119: 94.
”לְֽךָ־אֲ֭נִי הוֹשִׁיעֵ֑נִי כִּ֖י פִקּוּדֶ֣יךָ דָרָֽשְׁתִּי׃“
(Psalm 119:94 HMT-W4)
https://accordance.bible/link/read/HMT-W4#Psa._119:94
After all, we should realise that when we first started learning English in school, we may begin with the dry bones of grammar, but we are not stuck there. Like the Spirit of God breathing on the dry bones life in Ezekiel's Valley of Dry Bones, those of us who are able to take English further will find a new lease of life, power and freedom in the way we are able use the language to communicate.