If your flashcards are divided into just two piles—the big one and the small one—you may need to refine your reviewing system or "algorithm". One very common system is the Leitner system (named after Sebastian Leitner, who introduced it in the 1970s). This system assumes a larger number of stacks (excluding the set of cards that have not been learnt yet, i.e. your initial 1000 cards).
In the Leitner system, the first stack or box contains the cards that you need to review every day. Cards from the first stack that you consider "learnt" move to the second stack, which may be reviewed every other day. Cards from the second stack that you consider learnt move to the third stack, which has a lower review frequency, etc. Gabriel Wyner published a detailed schedule in this book Fluent Forever; you can find a "box schedule" on his website (although this does not entirely replace the description from the book).
With regard to the number of cards you review per day: this is highly individual. It depends on memory performance, which varies with age, physical fitness, motivation, etc. Strictly speaking, it is different every day! It also depends on how "memorable" the flashcards are. Gabriel Wyner, for example, discourages the use of translation-based flashcards and recommends using images, colours, etc. He also recommends that you make them yourself; simply producing your own flashcards is part of the learning process.
The bottom line is that you need to find out for yourself how many new words you can learn per day. According to research, "a typical learner should meet a word about 8 to 10 times to obtain full word knowledge" (F. Rasouli and K. Jafari: "A Deeper Understanding of L2 Vocabulary Learning and Teaching: A Review Study", International Journal of Language and Linguistics, 4.1 (Jan. 2016), emphasis added). In an article I cited in a related question, Rob Waring and Paul Nation ("Second Language Reading and Incidental Vocabulary Learning", 2004, emphasis added) noted:
Most research data we have looked at suggest that learners will learn
about 3-6 words per hour of reading. If we assume that a student in
school has 3-4 hours of exposure to English each week for 40 weeks a
year, and one third of that is reading, this totals about 50 hours of
reading per year, or vocabulary growth of between 150 to 300 words per
year, not counting natural forgetting from the reading alone.
Vocabulary learning from flashcards may be faster, but I don't have any data on how much faster.
You can also "delegate" the scheduling of the reviews to a spaced repetition system (SRS) such as Anki. In Anki, you can then tweak the settings for the number of new cards and the total number of reviews per day.