Here's a few ideas to get you thinking in a little more detail...the general theme is development of a three- or four-year plan for the time between now and when Megacorp whisks you, the new graduate, off to your dream job.
For a start-up IRA, a mutual fund account is the way to go. You can set up a mutual fund account online with Fidelity, Vanguard, T. Rowe Price or many others.
Many on this board are partial to Vanguard, which has a well-deserved reputation for low fees and expenses. (With low expenses on an account or on a mutual fund within an account, more of your money stays YOUR money.) An expense ratio below 0.5% per year is good. Less than 0.25% is outstanding.
Your initial deposit and your subsequent contributions can go into a money market account or directly into one or more mutual funds you choose. (You choose this at the time you set up the account.) My advice is to skip the money market step if you can and pick one mutual fund that has broadly diversified holdings allocated across several investment areas. A target retirement fund is one straightforward possibility. A total market index fund is another.
When setting up your account, you need to tell the mutual company what to do with the profits that will be returned to you periodically (in the form of interest, dividends and capital gains). Pick dividend reinvestment, which means that you want the company to pay you in the form of more shares of the mutual fund.
Stick with your initial choice for several years. As you review statements, quarterly reports and other correspondence from the company, you will absorb some of the ins-and-outs more experienced investors can take for granted: share price fluctuations, asset allocation, dollar cost averaging, the various types of distributions, tax categories associated with the distributions (although with a Roth you won't owe taxes), the effects of compounding, etc.
By the time you graduate, you will have established a good-sized starter nest egg that can continue compounding for you throughout your working life. Whether you will want to continue contributing immediately after you graduate is a bridge to cross later: if your employer offers a 401k plan with matching, that's generally the best place to save for retirement, at least to start.
I would hold off on immediately making the townhouse pitch to dad. Do some more research until you are confident you have identified all of the costs of ownership and outlined a monthly housing budget. There's much more to it than picking the house, negotiating the purchase price and paying the mortgage. The biggest continuing expenses will be real estate taxes, utilities, insurance and - for a townhome - monthly homeowners association dues and / or maintenance fees.