I always suggest that, at an absolute bare minimum, people start out saving/investing at least 10% of their gross income. However, that is generally for people who are just starting out in the "work world" and may not be making a lot of money, have student loans and need to keep a roof over their head, etc. It is also intended for people who are just starting to work on saving because it is imporant to develop the habit of saving without getting frustrated and feeling like you aren't able to live your life in the name of saving, as this could cause you to stop saving because you want to spend more money now. At the heart of it, the rate at which you set aside money to save/invest is nothing more than a decision about how much income/spending you are willing to forego in the present to help you have a comfortable retirement in the future. Delayed gratification can be hard, but it is vital unless you want to work until the day you die or have to rely only on Social Security for income.
As you grow in your career, your savings rate should grow as well, because in reality, only saving 10% of your gross income over a career is probably not going to be sufficient to sustain you in retirement at a level even close to what you were making while working.
I normally suggest that if someone can save 15% a year for their entire career, then they should probably be all right (though there is no guarantee that that is the case, because it depends on your goals and lifestyle "requirements" you plan for in retirement, as well as multiple other factors).
Obviously, the more you can save, the better off you will be in the long run. I've heard people complain about not having enough money saved, but I have never heard anyone complain that they saved too much.
If you can afford it right now, I would suggest targeting 15% of your gross income for savings (if you can afford, more, that is fine too). Then raise it periodically - for example, if you get a 2% or 3% raise each year, increase your savings rate by at least 1% until you hit 20% (then decide if you want to take it to 25%, and so on).
If you have a company 401k and there is a matching component, you can factor that into the equation (for example, if they match 100% of the first 5% set aside, you could set aside 10%, get a 5% match, and effectively be at a 15% savings rate); however, in a perfect world you will calculate your savings rate based only on the income you personally set aside, and any company match is icing on the cake (realistically, it just a more conservative way to deal with, and calculate, how much you are saving).
Additionally, before focusing too heavily on investing, you should make sure to set aside at least 3 months of living expenses (depending on your situation you could go as high as 6-18 months of expenses, but 3 months should probably be the bare minimum) in a savings account for an emergency fund. That being said, you can work on establishing an emergency fund at the same time you set money aside for investment (and you probably should, especially if your company offers a 401k match) - as long as the total reaches your savings rate target.
Please take the above as guidelines, since every situation will be different. Some people will only be able to save 5-10% for a while (and something is better than nothing because one of the keys is to get in the habit of saving) while some people might be able to comforatbly save 30%+ of their gross income and be just fine. Ultimately, you have to decide how much you can save and still live a reasonable life (i.e. you shouldn't become a hermit or a pauper just to save 20% vs. 15% or something like that), but in your case (from the information provided), I would probably suggest targeting a minimum of at least 10%...15%+ is even better.
Hope that helps and good luck!
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