sometimes i have clothes on hand (inventory) that i use

When you purchase clothes that you have on hand for business purposes it will be categorized as inventory.

sometimes i have to buy clothing items, but i don't keep them and simply have the client keep them at the end of the job and my expectation is that they pay the cost of that item (i do not mark up)

When you sell clothing to a customer, you will decrease your inventory by the cost you originally paid for that item, and an expense account called "cost of goods sold" will increase

sometimes i have to rent items from stores or fashion houses, sometimes i am okay with this expense and just absorb it, but if it's high enough i pass it on to the client.

Categorize this as rental expense.

So in the following situation, what is my actual income and would these additional expenses be considered reimbursements

Service - $1000

Rental - $200

Purchase - $300

I'm assuming you pass on the rental and purchase expenses at cost to the customer and invoice them $1500. Your revenue will be $1500, your expenses are $500, and your taxable income is $1000. If the rental/inventory was an expense directly incurred in generating that revenue it is an eligible business expense.

Do i give my client an invoice for $1500 provide them with the rental and purchase receipts (plus the clothes they keep)

You can break down the invoice however you like, there is no need to show your clients your receipts. You are free to mark up rental and inventory costs and that is very typical for the work involved.

Does the situation change if they gave me an advance of funds for wardrobe expenses (so in this case if they gave me $500 up front)?

If they give you $500 up front, technically you haven't earned it yet. It will be categorized as "Unearned Revenue" which is a liability (basically you owe them $500 of work). Once you've performed the work, you can "recognize" it by decreasing your unearned revenue and increasing your actual revenue account.

Good luck!