First of all, its good that you get different advice because it will start you down the path of learning to analyze and decide what is the best path for you, every person/family is different. Your risk tolarance is different, the risk of you losing your job, having an unforseen expense, those are different for each person. This is a good place to look at all the options and how different people handle it. Then you can deterimine what is the best way for you.
This is how I handle my Roths/Emergency Fund...First this probably isn't something you should do until you have a fairly large asset base (>$50K/100K/250K/500K/you pick).
I have a total of 5 "investment" accounts that I have direct control over. 1 taxable, 2 roths, 2 traditional IRA's. (wife/me).
1. I do not have an "emergency fund". My asset allocation is such that I have more than enough in "bond/reits/stocks/foreign/miscs...". I also keep my asset allocation based only slightly on what account the money is located. Over all it is "global" allocation across all 5 accounts. I do pay attention to taxable vs. IRA accounts and put specific things in each that make the most sense. (dividend in taxable, reits in IRA and so on).
2. I fund my R-IRA on January 2nd out of funds in my Taxable account that are invested to my selected asset allocation. During the transfer I have to sell the stock/bond fund/move cash/whatever and then transfer the cash to the Roth and purchase other or the same investments I was holding in the Taxable. This is where I usually take a moment to rebalance. The overhead on doing this is very very tiny. ($5 a trade, maybe costs me $30 a year tops, to shift things around within the 5 accounts)
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You are at the beginning stages of investing (everybody starts there). Right now, you have two competing goals. Fund the EF, fund the Roth.
First stage, fund the Roth with every $ left, use the Roth as your EF.
Second stage, fund the Roth to max before year ends, save rest of $ left as EF, Jan 2nd, use EF to fund Roth.
Third stage, fund the Roth to max Jan 2nd, EF still funded, save rest of $ into a taxable account.
Fourth stage, fund Roth Jan 2nd from taxable, merge EF into Taxable, safe rest of $ into taxable.
Fifth stage, retire early.
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Basically I don't "save up" money in the bank to be put into a Roth, I invest all unallocated $$$ into my taxable account based on my asset allocation. I then transfer the money into the roths the minute I can. The quicker you can put money into a roth the faster you begin your gains tax free. At the same time, there is no point sitting on 10K of cash waiting to invest it into the Roth Jan 2nd when you can, instead invest it now, and then transfer it to the Roth Jan 2nd.
You can't "catch up" on money you failed to put in your Roth, so if you don't put money into your Roth this year, you can't put extra in next year. This is why I would recommend you fund your Roth NOW. The only place I would put $ in before is:
1. 401K up to matching $
2. 401K with good investments (hard to find)
3. Debt that has a high interest rate. (you pick what high means)
You can always use the Roth as your emergency fund if you need to. Until you have a large asset base I would be careful investing your emergency fund/Roth in stocks. If you have a $10K Roth/emergency fund and you invest it in the market and you are down 30%, 7K may not be enough to cover that emergency. As your net worth grows, you will begin to grow a taxable account, create an asset allocation that has many different invest "classes" that do not move with each other.
Once this reaches a certain size you can "merge" your emergency fund/roth into the taxable as a part of your asset allocation. Fairly quickly I would invest the Roth into stocks and call your taxable the emergency fund. You want to put your biggest growth items into the Roth since any gains there will be tax free...
So I would hold the Roth/Emergency fund only until you can fully fund your roth and build an emergency fund at the same time. While your Roth is your emergency fund, you can invest the non emergency fund portion into stocks. ie. if you have a 20K Roth balance, and you only need 10K EF, then put 10K into stock investments and hold the other 10K in something "safer" until you can build an external EF.
Once you have an 100K "emergency fund". Having it invested in stocks/bonds/reits/"anything better paying than a MM" probably isn't going to hurt you.
Laters,
-d.