Snsdfan, it appears you have what's called a low-tech (actually zero-tech) tank. Which is not really my specialty, I'm more of a high-tech guy. But I'll comment where I can.
In brief, let me start by saying that the biggest limit to your plants right now is not the kind
of bulb you have installed.
Gravel is adequate, but not optimal. Some plants appreciate a finer substrate that they can really sink their roots into. In addition, gravel is completely inert, it does not adsorb or hold on to nutrients where the roots can get at them. Substrates made of fine, fired clay chips are a common alternative; they are both finer and hold on to nutrients. Fluorite is a popular choice. There are other and cheaper alternatives too (Soilmaster Select, Schultz Aquatic Plant Soil, etc.) I used a variety of substrates in my tanks, including some with gravel.
Fish and current plants are fine.
pH is oddly low. Some people claim at this point or a bit lower, it will start to interfere with the biofilter's ability to process ammonia into nitrite and then nitrate, though I haven't noticed it myself at this pH.
Nitrite should always be 0 unless the tank is cycling, or undergoing a mini-cycle as the result of new fish additions. Other possibilities - tank is overstocked, filtration or filter media dirty or inadequate, pH interfering with biofilter, bad test kit, etc.
As for the plants you're considering adding, I would skip the baby tears given your current tank, as they prefer high intensity lighting. Also, anubias are naturally slow growers, and may grow so slowly in your tank that they might not appear to grow at all.
Now to the real meat of the matter. Plants require light, nutrients, and CO2 to grow.
You currently have low light, and appear to have no added nutrients (other than fish food/waste) or CO2. Naturally with low light, your plants are going to grow slowly; and they are probably suffering from some nutrient deficiencies which further limit their growth and health.
Your plants will benefit from some added nutrients to eliminate deficiencies. As long winded as I am, that is a huge topic in itself that I won't attempt to describe here - so I suggest checking the articles section here as well as various posts and stickies.
Your plants will also benefit from some added CO2, as there is very little natural CO2 in aquarium water. Producing it from yeast and sugar (DIY CO2) is a cheap and easy method for small tanks like yours. As an alternative, at this light level plants can use Flourish Excel instead of CO2 to some degree, although real CO2 is definitely more effective.
Want even more growth? Add more light. But as you add more light, then adding more nutrients and real
CO2 (not Excel) to match becomes much more critical. The further light goes up, the greater the chance of any deficiency - even a transient
one - to cause algae problems.
More light opens up new possibilities as far as what plants you can successfully grow (like the baby tears and anubias), but also requires more skill and effort on your part.
More specific advice really depends on your personal expectations and comfort level. Some people are perfectly happy with zero-tech tanks.
Decide where you want to go, read up a bit on the topics I've summarized that interest you, then post any specific questions you have. We'll be here.