| all your plants will grow well in the water (although i have no experience in the guppy grass so cant vouche for it)! The possibility of the whole tank being overcome by those specific plants could only happen over time, as long as your trimming them & getting rid of the excess on a regular basis its nothing that will happen overnight.
as far as anchoring your plants many pet shops sell plant anchors that come in 6 or so packs which are just like twisty ties only made of lead that you can wrap around the base of a plant and it'll stay held down. Otherwise maybe you could put in a good sized stone/rock to hold your plants down? I wouldnt do that unless your tank is a good enough size though...10 gal or so.
Although I would also like to comment that i use hornwort for my tanks, and i leave it floating. The babies seem to love it floating and they hide very well in it, it appears to work out quite nicely. The fish stay completely safe and grow fast, and since it floats when i feed they can even eat while they stay in the safety of the hornwort (i dont serperate my fry from the tank, they stay in with the big boys til they grow). In fact the only problem really that i can think of as far as keeping the hornwort floating is if you have a hang-on filter, it seems to get clogged in the filter intake pretty regulary unless you can control the current to keep the hornwort staying on one side. I have a section of val plant that is tall enough to keep the hornwort in its own area, away from the suction of the filter intake | 
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You can float it, so you can still make sure that you keep the bottom of the tank clean.