First job out of school and a move to a new city? In your shoes, I'm renting. Something inexpensive that's month to month or on a short term lease and close to work. When I have been on the job a couple of years and think things are stable for the long term, then I would look at buying.
The problem is that there aren't any rentals available like that. From what I've been told and have seen, the rental market is very supply constrained. All of the rental homes have stable tenants and never come available, and few apartment complexes are available. The apartments that
are available are going for $1,000 - $1,200 and available a few exits down the interstate. For comparison, there are homes selling for $80,000-$100,000 that fit my needs (and then some) within a 5 minute walk to work. As well, the homes for sale are in the middle of town within walking and biking distance of anything I'd need, whereas the apartments are deliberately located away from everything, outside of town in a "planned community" setting.
If I could get a yard and live in an area I liked while renting, I'd scoop it up in an instant and forego the headache of buying/owning. But buying appears to be the only way to make that happen, so is the way I'm leaning towards. As well, if I buy during my relocation instead of waiting a year then housing hunting expenses and closing costs will get reimbursed as part of my relocation package.
Lots of major life changes all at once can be really stressful. A new city/moving and a new job (after a lifestyle of school) are pretty big items already. Not sure I'd want to add buying a house to it.
While it can be stressful, delaying it doesn't necessarily diminish that stress. House hunting, buying a house, packing up, moving, unpacking, and settling in to a new home is significantly less stressful when done during the few weeks of downtime between graduating and starting my job verses if I were to try to do it all while working a year or so later. Not to mention waiting is more expensive, since I'd be footing the cost of the second move.
I too would be hesitant to buy in a new, unfamiliar city at a new job. You probably don't know how much you'll like your job, or how stable your employment prospects there are...
In some big cities, it's possibly to find rental opportunities that don't need you to sign on for a year. You might consider searching for some of those; craigslist is great for these kinds of things.
While I don't know how much I'll like my job and can't vouch for certain regarding stability, neither of those are top concerns for me. The company is fairly tenured and is trying very hard to attract younger talent, part of which is encouraging internal moves every 18-24 months until you find the niche you like the most. So even if I don't like my initial role it's not only acceptable but encouraged to look internally for something I may like more, providing stable employment and negating potential issues regarding job dissatisfaction. Out of the college hires within my group over the past 10 years, all but one are still with the company (so I was told).
It's also not a bigger city, but rather a mid-size (~50,000 person) city in the Midwestern US. Combined with the constricted rental market, the only leases I've seen available are for 12 and 15 month terms.