It sounds like you are single and covered by a retirement plan at work (your 401k).
For 2015, you can contribute the maximum amount ($5500) to a Roth IRA until your MAGI reaches $116K. Above $116K and below $131K, you can contribute an amount between $0 and $5500. This is called the phase-out range. I believe but am not certain that it is a straight-line reduction, meaning that since the phase out range is $15K, for each $3K in additional income the amount you can contribute is reduced by $1100 ($15K / $5500 == $3K / $1100). Above $131K, you cannot contribute to a Roth IRA.
If you end up contributing more than you are entitled to do, you can recharacterize the excess contributions (plus any associated earnings) from your Roth IRA to a traditional IRA; in that case no additional taxes are due. You can also withdraw the excess contributions plus any associated earnings from your Roth IRA; if you do that you will owe taxes plus a 10% early withdrawal penalty on the earnings (but not the contribution) if you are under 59.5. (You can technically leave it in the Roth IRA, but pretty much nobody ever does that because you have to pay 6% of the excess contributions every year that you leave the excess contributions in the Roth IRA.)
You can also go the other direction -- open and contribute the maximum to a traditional IRA, and then recharacterize some of your contribution (plus any associated earnings) to a Roth IRA.
Note that you can contribute to both accounts, so supposing you made $119K next year, you would be $3K into the phase out range, so you could contribute $4400 to a Roth and $1100 to a traditional.
There are time limits to doing the recharacterization; I don't recall offhand what they are. I am nearly certain that you may recharacterize 2015 contributions any time before you file your taxes for 2015 in April of 2016.
Finally, note that although you can contribute to a traditional IRA with any income, you can only deduct your contributions from your income if your MAGI is below $71,000. Based on your income, it looks like you would not be able to deduct a contribution to a traditional IRA. Given that, a Roth would be a much better choice -- in either case you won't deduct the contribution, but with a Roth your withdrawals would be tax free but with a traditional IRA your withdrawals would be taxed at ordinary income rates.