Welcome!
If you're wanting to keep cost down, I'd recommend washing your own diapers and skipping the service. Washing cloth diapers is really not hard or time consuming like it seems it would be. I know I was the most worried about doing diaper laundry when we first switched to cloth, because I really disliked all laundry in general. However, I was pleasantly surprised to find how easy diaper laundry is, in fact I even liked it! I really detest all other laundry(so glad I have older ones to do it all these days), but I LOVE doing the diaper wash and never mind it a bit. It takes maybe 15min of my actual time 2 or 3 times a week. It's as easy as throw the diapers in the wash, do a cold rinse, a hot wash/cold rinse cycle with a tiny bit of detergent, and a 2nd cold rinse. Then toss everything in the dryer(or pull out covers to hang dry that need that). All of the stuff I use can stand up to hot washes and hot machine drying, so it's really super easy. I find it very satisfying to take a load of fresh, warm clean diapers out of the dryer and fold them all in a nice neat stack, but you can even skip the folding if you want and just toss them in a basket to keep at the changing area and grab one as you need it. It's easiest to use a dry pail, and if you use a pail liner you won't even need to clean the pail out. Just lift the liner and toss it in the washer with the diapers. It's nice to have 2, so you can have a clean one while the other is in the wash.
As far as flushable liners.. I know some people really like them, but for us they didn't work that great. Maybe my babies were at a too squirmy age when we tried them, but often the liner would bunch up and poop would get on the diaper anyway. The liners almost never caught all the mess for us. What I like better is having a diaper sprayer. It's a little gadget similar to a kitchen sink sprayer that hooks to the water line on the toilet. It's extremely easy to install, only takes about 10min. I'm using one I got for $26ppd off of ebay, and it's working great. If you search for cloth diaper sprayer on ebay, you should be able to find it. I really, really love having the sprayer for once my babies are on solids. For breastfed only stools there's not even a need to rinse... just toss the poopy diaper in the pail then directly in the washer on wash day. Breastmilk stools are water soluable and easily dissolve and rinse away in the initial cold water rinse. If you are blessed with a toddler who has really nice and formed poops that are "ploppable", lol, then you can probably get away with just shaking the poop into the toilet with no rinsing. I've not been that lucky, so a diaper sprayer for us it is!
I don't know about the GDiapers first hand, but most of what I've read about them has been negative. I think if you do a search on here for them, you could find out more.
My 15mo has figured out how to remove her diapers too. I've learned to put her down for a nap in a well pinned prefold with a snapping cover(Motherease Airflow) or a pull on cover. She can't get those off near as easily as velcro ones. However, I still use the velcro ones during the day when she's being watched more, and it's fine. I know this place makes side aplix diapers which seems like would be more difficult for a baby to take off.. maybe that would be an option for your little houdini
http://www.lucyshopechest.com
The best place to start when you're trying to decide which diapers to get is to figure out your diaper budget. Prefolds and covers are the cheapest, and fitteds, aios, and pockets are more pricey. Also, think about your personal preferrences. Do you like snaps better or velcro? Front snapping, or side snapping? If you're not sure, I'd recommend trying just one or two of a few things to see which you like best before you order a whole bunch of any one thing. Most places have some sort of starter package with a little of this and that, so maybe that would be a good place to start.
If you're wanting to keep cost down, I'd recommend washing your own diapers and skipping the service. Washing cloth diapers is really not hard or time consuming like it seems it would be. I know I was the most worried about doing diaper laundry when we first switched to cloth, because I really disliked all laundry in general. However, I was pleasantly surprised to find how easy diaper laundry is, in fact I even liked it! I really detest all other laundry(so glad I have older ones to do it all these days), but I LOVE doing the diaper wash and never mind it a bit. It takes maybe 15min of my actual time 2 or 3 times a week. It's as easy as throw the diapers in the wash, do a cold rinse, a hot wash/cold rinse cycle with a tiny bit of detergent, and a 2nd cold rinse. Then toss everything in the dryer(or pull out covers to hang dry that need that). All of the stuff I use can stand up to hot washes and hot machine drying, so it's really super easy. I find it very satisfying to take a load of fresh, warm clean diapers out of the dryer and fold them all in a nice neat stack, but you can even skip the folding if you want and just toss them in a basket to keep at the changing area and grab one as you need it. It's easiest to use a dry pail, and if you use a pail liner you won't even need to clean the pail out. Just lift the liner and toss it in the washer with the diapers. It's nice to have 2, so you can have a clean one while the other is in the wash.
As far as flushable liners.. I know some people really like them, but for us they didn't work that great. Maybe my babies were at a too squirmy age when we tried them, but often the liner would bunch up and poop would get on the diaper anyway. The liners almost never caught all the mess for us. What I like better is having a diaper sprayer. It's a little gadget similar to a kitchen sink sprayer that hooks to the water line on the toilet. It's extremely easy to install, only takes about 10min. I'm using one I got for $26ppd off of ebay, and it's working great. If you search for cloth diaper sprayer on ebay, you should be able to find it. I really, really love having the sprayer for once my babies are on solids. For breastfed only stools there's not even a need to rinse... just toss the poopy diaper in the pail then directly in the washer on wash day. Breastmilk stools are water soluable and easily dissolve and rinse away in the initial cold water rinse. If you are blessed with a toddler who has really nice and formed poops that are "ploppable", lol, then you can probably get away with just shaking the poop into the toilet with no rinsing. I've not been that lucky, so a diaper sprayer for us it is!
I don't know about the GDiapers first hand, but most of what I've read about them has been negative. I think if you do a search on here for them, you could find out more.
My 15mo has figured out how to remove her diapers too. I've learned to put her down for a nap in a well pinned prefold with a snapping cover(Motherease Airflow) or a pull on cover. She can't get those off near as easily as velcro ones. However, I still use the velcro ones during the day when she's being watched more, and it's fine. I know this place makes side aplix diapers which seems like would be more difficult for a baby to take off.. maybe that would be an option for your little houdini
The best place to start when you're trying to decide which diapers to get is to figure out your diaper budget. Prefolds and covers are the cheapest, and fitteds, aios, and pockets are more pricey. Also, think about your personal preferrences. Do you like snaps better or velcro? Front snapping, or side snapping? If you're not sure, I'd recommend trying just one or two of a few things to see which you like best before you order a whole bunch of any one thing. Most places have some sort of starter package with a little of this and that, so maybe that would be a good place to start.