you may need to get a co-signor depending on how much time has past since your eviction. It would also help to talk to the management company and ask them what they would require.
I would recommend a couple letters of reference, a letter explaining why you were evicted (was it due to loss of job, change in life?) and be prepared with a larger down payment.
Many people have had a difficult time financially, don't feel like you're alone here and the only one who's gone through this. Its the past, so now work on the future and hopefully towards home ownership which is where you"ll really start saving money and building equity.