I've read that a lot size is 100 shares of stock and that if you trade in lots you have a better chance of getting a good price on your order. Is there a similar thing for options contracts? In other words, would it be better for me to trade 10 orders of 100 options contracts, or one order of 1000 options contracts?
There are a number of rules regarding the routing odd lot orders for stocks and the end result is that they often take longer to complete than round lots. None of this has any bearing on option orders.
With options, a fill is dependent on there being a counter party willing to trade at your price in the size that you are seeking. If there isn't one, you'll get a partial fill or no fill at all.
Off hand, I can think of two reasons for placing an order for 1,000 contracts rather than 10 orders of 100 options contracts (you're quite the player, aren't you? :-).
First, there's timeliness. If you place a partial order, price may move for or against you by the time you get a fill. For a must have position, do 1,000 contracts at once to help avoid missing out on a complete fill.
Second, there's commissions. If you are paying a base of "X" plus "Y" per contract then 10 separate orders will incur 10 base rate fees and your total commission outlay will be higher. If you pay a flat fee per contract then it won't matter at all.
If you believe that displaying your entire order might affect price in some way and if your broker offers them, you can use a Hidden Order to completely hide the size of the submitted quantity from the market.
A single contract is fine.
Options usually have a multiplier of 100, so a single option contract will give you exposure to 100 shares of underlying. There are in some cases "mini" and "jumbo" contracts for 10 and 1000 shares respectively though options are less liquid than the regular sized contracts.
100 shares or more allows your order to be displayed on the 'tape' (the consolidated market data feed used by the exchanges). As a result, if your order is posted there, the exchanges and their participants have to trade against it before trading at a higher price (if the order was a sell) or trading at a lower price (if the order was a buy). This is the order protection rule.
If the stock is liquid and there is likely to be someone else on the same exchange with more than 100 shares at the same price, then you may not find a reduction in execution quality for using an 'odd-lot' size of less than 100 shares.