As far as travel goes:

 For tax purposes, travel expenses are the amounts you spend when you travel away from your tax home overnight for your business (rental) activity. You don’t have to travel any set distance to take a travel expense deduction. However, you can’t take this deduction if you just spend the night in a motel across town. You must travel outside your city limits. If you don’t live in a city, you must go outside the general area where your tax home is located.

See this article for more information on travel for rentals. 

https://www.nolo.com/legal-encyclopedia/deducting-landlord-out-town-travel-expenses.html

Below is a detailed explanation of how to handle the property purchase.

The only deductible closing costs are those for interest, and deductible real estate taxes. Other settlement fees and closing costs for buying the property become additions to your basis in the property. These basis adjustments include:

    * Abstract fees,

    * Charges for installing utility services,

    * Legal fees,

    * Recording fees,

    * Surveys,

    * Transfer taxes,

    * Title insurance, and

    * Any amounts the seller owes that you agree to pay, such as back taxes or interest, recording or mortgage fees, charges for improvements or repairs, and sales commissions.

    * Those costs that are basis adjustments can be part of your yearly depreciation deduction for the rental property.

For additional information, refer to Publication 527, Residential Rental Property, Publication 17, Your Individual Income Tax Guide, and Publication 535, Business Expenses. Several closing costs cannot be deducted and are not added to basis. Please see Publication 527 page 12 for more information.

  The following items are some settlement fees and closing costs you cannot include in the basis of the property.

   1. Casualty insurance premiums.

   2. Rent for occupancy of the property before closing.

   3. Charges for utilities or other services related to occupancy of the property before closing

    4.Charges connected with getting a loan. The following are examples of these charges.

        Points (discount points, loan origination fees).

        Mortgage insurance premiums.

        Loan assumption fees

        Cost of a credit report.

        Fees for an appraisal required by a lender.

    5.Fees for refinancing a mortgage.

If these costs relate to business property, items (1) through (3) are deductible as business expenses. Items (4) and (5) must be capitalized as costs of getting a loan and can be deducted over the period of the loan. 

  Also, do not include amounts placed in escrow for the future payment of items such as taxes and insurance.