Buying Slabbed Coins

For Mercury dimes, I recommend Denver mint issues from 1938-1945. These are abundant in gem grades and are universally well struck. They're also pretty cheap because the mintages are high and they were saved by the roll. It seems like I see tons of really nice 1939-D, 1943-D and 1944-D in particular, and all these dates are modestly priced.

Go ahead and be really picky about the quality of the strike, etc. because there are lots of these out there to choose from. Look for the FB designation which means the central detail is well struck and fully detailed, but also look at the peripheral lettering, the last digit of the date, and low-profile elements to see that they're well struck and crisp. If you shop around, you can find one to fit any tastes, satin, frosty, lustrous or proof-like strikes, blazing white or beautifully toned.

San Francisco and Philadelphia dimes from that period are similarly inexpensive but usually not as well struck and attractive.

For Walking Liberty halves, you'll probably want to restrict yourself to coins from 1939 to the end of the series - older ones are going to start to get pricey in higher grades. The series tends to be poorly struck, so look for ones that show full detail in the high points - Liberty's chest, head and left hand. My understanding is that Philadelphia minted walkers from that era have the best strikes, but I am not as familiar with the series.

This seems like a pretty decent deal, though certainly better can be had:
http://www.ebay.com/itm/1944-D-Merc...em19c868c524

This too:
http://www.ebay.com/itm/1944-D-Merc...em4cf9c13e2b

This is a gorgeous half, even if it's priced strong for the grade - my hunch is that it's undergraded (perhaps others more knowledgable than I can weigh in on these!)
http://www.ebay.com/itm/1944-S-Walk...em45fd40ddd9

I should mention - I don't know any of these sellers, I just picked random coins off of ebay to illustrate my previous point - and to give you a good start. =)

@delaner: The '44-D dimes look good, but I think the OP is looking for a more modest grade. It will probably be harder to find as many in MS-64 because most of the later date Mercury dimes are not worth slabbing unless they're MS-65 or better.

The walker half is lustrous, but it's got a really poor strike; there is a lot of missing detail on both sides.

Here's an ebay search for auctions ending in the next few days for dimes that match your criteria. Just be patient, and wait for a nice one with nice pictures to show up at a reasonable price.

Another date to consider for Mercury dimes is 1916 (Philadelphia only - 1916-D is prohibitively expensive and 1916-S is a bit more expensive and tends to have somewhat poor strikes). 1916 was saved in large numbers and had a pretty high mintage, so they're still reasonably priced at grades up to MS64FB, and you can find very nice, well-struck examples. Due to design changes in later years and wear/damage to the master hub, they are more detailed than later dates. Look for one with well struck peripheral lettering and full detail in Liberty's hair on the obverse, which is one area that can be weakly struck on this date. Many have also developed a beautiful patina - here's a beautiful 1916 that sold recently; I would loved to have owned that one!

Thanks for that, fwiffo! Surely is helpful...

Yes, premiums seem to me to go PCGS > NGC > ANACS > ICG

As a general rule at coin shows you will always hear a dealer say "Of course that one cost more, it's in a PCGS slab". Many people like to have their coins done by PCGS or NGC due to that alone I suspect. There are virtually hundrds of TPGS's out there now. If you look up TPGS's on Google, you would be amazed at how many there are and how fast they just vanish.
Not sure why you want a slabbed coin anyway. Almost always your going to pay for to get any coin in a slab and that really does not make the coin any better. For average coins like your looking for, I'd simply look into regular coins unless your neice just wants the slabbed thing. If so, might just as well look into some of those normal, everyday coins people send in for slabbing. I've seen many coins worth $1 in a slab.

My niece was wanting them slabbed but after considering, I think I might just go for a high grade raw Mercury and a slabbed Walker. She really wants the Walker slabbed, even after some prodding from me to get both raw, so her reasoning isn't especially important to me. I have to keep my reputation as the good uncle.